We should do an ATOT get together! Heh.
Restaurants:
Go to Greenhouse Tavern and order the pig's head. No, really.
Momocho is also very good, and not your typical mexican restaurant.
Melt has great sandwiches.
Other random stuff:
Go see a play - Playhouse Square is the largest performing arts district in the US outside of New York.
Good basketball for cheap - Cleveland State almost knocked off Kentucky over the weekend. Campus is right downtown next to Playhouse Square.
Greenhouse Tavern is ok, but I wasn't super impressed with it. Personally I prefer Lola right next door. Also, Brasa is a Brazilian steak house that is supposed to be great. Over on the east side is Bodega which is a pretty good place.
For restaurants around Cleveland as mentioned Melt and Hot Sauce Williams are featured on food channels quite often. Michael Symon has restaurants around the Cleveland including Lola's, Lolita's, and B-Spot. I have never ate at Lolas or Lolitas myself but B Spot has some absolutely amazing burgers, the Fat Doug is my personal favorite.
For restaurants around Akron I would definitely recommend you check out the Diamond Deli, the Old Bald Guy is absolutely delicious. Mr. Zub's also has some very good food. If you are looking more for a dining experience there is Crave, Bricco, and Cilantro. The Lockview is also known for grilled cheeses (such as Melt, though in MUCH smaller portions) but part of the appeal to Lockview is their drink selection also.
I personally have little to no experience in the more expensive restaurants around Cleveland, so I can't help you if you are looking for something real fancy.
Melt is good, but expect an hour+ wait on Friday/Saturday nights. B Spot is also usually pretty busy. Both are good, but they are very different types of places. Melt is the reason the Midwest is so fat. Each sandwich is cut in half, and one half is plenty for most people. The full sandwiches are simply massive. B Spot is more of just a solid burger joint. Plus you can get all sorts of toppings. And they have various ketchup type sauces for the fries (which are the thinner style). Lola is a higher end place compared to Lolita. I have not been to Lolita, but I hear it's good. Lola I can say was pretty good. It was a really enjoyable dinner.
In Akron, for sandwiches go to Pub Bricco in Merriman Valley, or do Lockview in downtown. Lockview's food is decent although Pub Bricco is better. Conversely Lockview has a way better drink selection (have a 5 page beer menu). Cilantro is pretty good for chinese/thai, but if you like sushi you have to go to Merriman Valley to Sushi Katsu. I like my sushi and my step dad (who lived in San Francisco and has traveled to Japan) who loves sushi both think it's the best sushi in NE Ohio. It's a very small place, but well worth it if you like sushi IMO.
My wifes family is from Cleveland so we head their every couple of years around this time.
Two of my favorite places to hit up are the West Side Market and while we are on that side of town I stop in at a small authentic Italian store called Gallucci's.
Tower City is kind of cool to see. It's a shopping mall now but at one time it was a train station so the architecture is really neat.
WSM is a cool place. Not as much fun in the winter, but it's a really neat place to see. Tower City is kind of meh anymore IMO (except for the architecture as you mention), although there is Cleveland square with the lights that is kind of enjoyable to walk around through.
Little Italy over on the East side is another good place.
TLDR version:
Food
Burgers - B Spot, Pub Bricco, Melt, Lockview in that order
Sit down (non-burger) food - Lola, Sushi Katsu, Green House Tavern, Bodega, Lolita, or Cilantro in that order as well
Non-food
Playhouse Square, Cleveland Orchestra, Trans-Siberian Orchestra will be in town (unsure if tickets are available) this weekend, usually a decent comedy scene at Hilarities or the Improv, a good wine bar (that also has food) is Rocky River Wine Bar over on the west side, History/Art museums, various sporting events, Microcenter on the east side (which has Legacy Village if you want to do some higher end shopping), House of Blues is right next door to Lola/Green House and usually has pretty good stuff going on,
or you could go see drunk west 6th girls.