Lots of good suggestions, here are the ones I usually recommend:

Dixie Chicken- It's the iconic bar of A&M complete with a true C&W atmosphere and a rattlesnake tank located at Northgate.

The other suggestions for nightlife are better than anything I could give as I have been out of school too long.

Best food imo:

Koppe Bridge for burgers or BBQ
J Cody's for a casual but amazing steak
Laynes for Chicken Fingers
Christophers for fine dining

On campus:

Driving down Wellborn and seeing Kyle Field, Blue Bell Park, and Reed Arena. Also the Student Rec Center is there which is a fantastic workout place for students and you can check it out.

Bush Library and Museum-Very cool if you have a couple hours. It's a first rate museum with some really cool stuff from GHWB's term like a walk through cut out of AF One and a section of the Berlin Wall as well as a lot of his WWII stuff.

MSC-Newly renovated and I haven't actually been there since the Spring when they reopened. This is the "living room" of the campus and home to the 7 Congressional MOH that Aggies have been awarded.

Corps Museum-If you are a military buff or just interested in A&M history it's fascinating. It's not very big so you can walk through it pretty quick. Also houses a fantastic gun collection.

Bonfire Memorial-Very powerful tribute to the tradition and the kids that died that day it fell. Reading some of the letters the kids had sent home prior to the tragedy talking about what A&M and Bonfire meant to them is hard to get through.

In terms of the town itself a lot of folks like to rag on it but it's really a nice and affordable college town. There are about 225k people in the Metro and it is growing at a nice clip. If you stay out of some bad parts of Bryan there is very little crime and everything revolves around the school. People tend to be friendly. If you wear gear from your SEC school you will also be greeted warmly by many Aggies and likely get more than a few free beers and folks wanting to strike up a conversation.