I'm guessing the Mexican is El Macho's and the pub is Dukes 92. Both are still they're but a good five/ten minute walk from the Dalton building.
Other options in the immediate vicinity.
Opposite the Dalton (so next to the BBC) is Kro2. A Danish owned bar that does great food. Nice outdoor seating as well. Service can be a little slow when it's busy. Very nice glass design of the place.
Turn left out of the Dalton and you have Odder, a new bar. The original place up in the Northern Quarter serves good food and I've heard that this place is pretty nice as well. I've only been for drinks but enjoyed it. Further along is a Revolution bar (OK, never eaten there), a Cafe Nero (and a Starbucks opposite) and then Monsoons kebab shop. Now, you may not believe me but this place is great!
Nicer food can be had further along at the Cornerhouse. They have a canteen style place so the food is served very quickly. Can be very good indeed. They always have nice soup and carrot cake.
If you turn right out of the Dalton building then you're in student land. There are a few takeaway places that range from grotty to OK but there is also a place called the Eigth Day (nest to the Poly student union). It's a veggie/health food shop with a great cafe downstairs. Lovely vegetarian food.
If you want a good pub, then the Lass O'Gowrie is on the side street left of the BBC (Charles Street, I think). At the top of that road is East-Z-East, one of the best Indian restaurants in town.