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1: If you chose to fly with Ana, as this walkthrough does, you'll land on a helipad in South Medina, just above a Queequeg's Coffee Shop. If you've got Sid Black as your pilot, you begin in Arcology Flight Bay 23, and you'll want to head to the South Medina Queequeg's hub pretty much right away, anyway.
2: Other than the semi-hidden multitool on the railing, head through the doorway and take the ladder up. Explore the small area here, reading the datacubes for some backstory and taking the energy cell on top of the locker. Head back down all the way and you'll be right across from the Queequeg's Coffee Shop. Speak with the manager to get a secondary quest, and then again with the Medina Sheriff to the right of the shop for a rough map (seen above) of the area. The Queequeg map point is a little off. It should be slightly up right against the square above it. That threw me off for a bit :).
3: Hang a left (south) and follow the signs to the Medina Apartments (eastward). Very soon you'll round a corner and be faced with a gate to North Medina. Transport there and climb the stairs after the first corner. On the balcony is Leo Jankowski and an Omar Trader. Talk to both for a quest, one to find out about the Templars for Leo and another for a suit of armor for Omar in Arcology. Head back down the stairs and continue along the path until you find the Order Mosque and its big doors on the right side. Along the way you'll get stopped by a charlatan, and I'd recommend saving your 20 credits.
4: We're going to skip the church for now. Beyond it and straight ahead on the path is a news holocomm. Head up toward it, read it if you wish and take a right, following the path until the end, which is a small square with a few people watching a holocomm of Her Holiness. Activate it if you wish, and if you played Deus Ex 1, perhaps her accent rings a bell? Hmm. Against a back wall is a wooden pallet hiding a grate. Break, move or shoot the pallet, enter the grate and crawl up its ramp and down the shaft to another grate. Don't open it yet.
5: Inside this room is a camera and man called a Harvester. They'll attack you if they see you, so open the grate, send in your Spy Drone to disable the camera, Cloak and head to the small chest on the right side, containing an energy cell and Increased Range Weapon Mod. Now slip back through the grate into the square with Her Holiness, back out toward the Order Mosque and continue along the patch up a set of stairs.
6: When you get to the top of these stairs, head around them to find the same Harvester behind the bars. Talk to him to receive a bounty quest to kill the security chief in Arcology. That's it for this floor. Take the next set of stairs up to level 3, follow the small outside hallway around until you get to the door marked Nassif, and enter. Inside is Maskini Nassif, an energy cell and some other items. Talk to him to get the code for the Tarsus Academy here, which is also in the Arcology building, and then take the next set of stairs up. to level 4.
7: Walk around until you see two barrels blocking a grate. Walk into the barrels, moving them aside and enter the grate. Take out the spider inside, and you'll emerge in a bathroom, but wait here. Two templar paladins are in the next room that you'll want to take down, however you wish. If you remain in the grate, they'll have a hard time getting at you. Afterward, read the datacube on the shelf in the next room for the Headmaster's Secret Room keycode, and read again the datacube in the back room for a bit about their spying project on Leo, just what he wanted. Take a look at the holocomm before you leave.
8: Exit back out the way you came and find your way back to Leo, near the entrance to North Medina. Tell him what you found and he'll offer a split of his bonus to you when it's over. Now go back to the Order Mosque and enter. Agree to the weapon lock, take a left at the first intersection, then a right into the huge central room, where Billie Adams and Saman stand talking. Speak with Billie, and if you have a chance, Saman multiple times. Otherwise, if he's not there, you'll find him and 100 locked credits up the stairway through the back doors of the central room. You can also find 50 credits under a desk in the same back area near the entrance to Arcology. For now, head back into the large room, back through the door you came through, and hang a right.
9: Go downstairs to the Infirmary and talk with Mrs. Ameer who will ask that you find a way to get her child enrolled in the Tarsus program here. Follow the corridor around back up another set of stairs and finally, back to the entrance of the Mosque. Exit through the main doors, head back to South Medina, walk past Queequeg's and hang a left. You'll see a sign for the Nassif Greenhouse, our next destination. On your way you'll get stopped by some Medina thugs whom you can pacify with 150 credits or fight. Continue on and enter the greenhouse, where you'll get an objective from Donna Morgan with different ways to destroy the food production.
10: As you enter the first room there will be a camera on your right and two doors, one for Hydroponics and another for the Nassif Warehouse. Disable the camera (Spy Drone, multitools or alt-fire on your Mag Rail) and enter the Warehouse door. Take down the security bot patrolling the area and notice the Hydroponics Air Filtration door at the other end of the room. Pick up an explosive crate in the room, set it near the door and fire at it with your gun to blow it open. Now take another explosive crate, set it near the filter and do the same thing, effectively shutting down the food production.
11: Before you leave, however, a few more things to do. In the Air Filtration room where you blew up the filter, a grate is revealed, Zelda style. Head through the grate shaft to a small room with a BIOMOD CANISTER, back out of the Air Filtration room and up the ladder in the Warehouse room into a small observing room. Take the items, view the holocomm of Maskini, and climb the nearby stairs to a triad of yellow beams. Use your Spy Drone or an EMP grenade to take them out, and enter the hall at the top of the stairs. You'll find a medbot and a far away security camera you can disable if you wish. Enter the nearby room across the hallway and read the datacube near a small cot for the computer access codes.
12: If you didn't blow up the filtration system before, you can alternately use the login you just received on the computer up the hallway near the camera to terminate the program. Whichever way you decide to do it - destroying the plants with fire is another - head out of the room with the code, and take a right to a balcony overlooking the square you entered at. Time for a jumping puzzle for the game's third secret weapon, the Hellfire Boltcaster.
13: Climb up on the right side of the balcony and look up and to the right. There's a ledge up there we'll want to reach. First, jump over to the ledge on the right side. Crawl under a set of protruding beams to the other side of them and stand up. Quicksave your game. Jump onto the first of the protruding beams and them mantle up the wall to find yourself on the ledge. I fell a few times in my attempts, which was why the quicksave came in handy. Once up, enter through the grate and crawl through the shaft to a small room. Behind a broken chair is the Hellfire Boltcaster, modified to fire incindiary bolts rather than tranqs.
14: Find your way back to the entrance, and exit the Greenhouse area. If you still needed to destroy the food production, you could always enter the Hydroponics door and use either your Hellfire Boltcaster or a flamethrower on the plants through the left door (and past a couple spiders). Exit the Greenhouse back to South Medina and follow the signs to the Arcology. Talk to the guard at the end to give him your Arcology Pass, the one you received from the Harvester for his quest. Alternately, you would have had one from Sid if you used him as your pilot. By the way, I found this at arcology.com:
An Arcology is based on Paolo Soleri's concept of the development of compact 3-D alternatives to existing urban sprawls, combining more efficient use of land and resources. In the future, mankind will be pressed closer and closer together in a vast urban sprawl. As society is deals with a rise in population and population density, while having to deliver a much more efficient use of resources, use of the arcology will become commonplace.