I third Seven on Prospect! I've never had a bad meal... but it is busy on weekends and you'll need a reservation. French Toast in Peoria Heights is also excellent - I've had a wonderful filet there. Both are on the high-end.
I couldn't recommend a single BBQ place in Peoria. I don't like any of them and would prefer to make it at home.
If you want something a little more original to Peoria I'd recommend Rhythm Kitchen downtown. They have a great menu, made-from-scratch desserts and great music on weekends.
Another burger joint to try is Khaki Jacks on N. Allen Road. They have excellent burgers, fries and drinks (I like the tuna steak and ostrich burger too).
4600 N Prospect Rd, Peoria, IL 61616
7223 N Allen Rd, Peoria, IL 61614
If you are looking for local and very creative cuisine, head to June in Peoria Heights. http://junerestaurant.com/ It is more expensive than most, but the food is exceptional. Chef Josh Adams was nominated for a James Beard award for 'up and coming' young chefs.
For Steak/American I would also suggest Peoria Heights. Both 'Jims Bistro' http://www.peoriarestaurants.com/restaurants/?restaurant=jims_bistro and 'Seven on Prospect' http://www.7onprospect.com/index.htm are very good.
Peoria does not really do BBQ well in my opinion.
I tend to like the local places and not the chains. These recs are at the higher end of the price spectrum, but should seem cheap after paying for college.
If you are in the mood for a burger and a great view of Peoria. Head to the burger barge http://burgerbargeinc.com/DIRECTIONS.... in East Peoria. You may see me stop by in our seaplane for a cheeseburger.
Let me know if you have any other questions.