We were in Montevideo last Christmas. You will quickly find you will have a tough time spending a full day of touring -- there's just not tons to see. As such, we'd tour morning/afternoon, and then hit a patio around 3-4pm for Pilsen beer and people-watching. One area we found consistently busy with locals was the Plaza Constitucion. The side streets are quite busy, and we ate at a very good small plates resto here (no recollection of the name), although it is primarily a drinking area.
We also spent an afternoon at La Pasiva (there are several around the city), basically a beer pub that serves hot dogs and other like snacks. The beer was cheap, again Pilsen, and it was entertaining to watch young professionals in suits, particularly attractive, thin women, gorging on 3-5 hot dogs with mayonnaise (warm -- on the table all day -- yuck!) with their large litres of beer.
Near the La Pasiva in the Plaza Constitucion, on the same laneway, was a trendy restaurant (again don't remember the name) that was fantastic. We enjoyed a Uruguayan red with our meal, and ate a lot of red meat. After, there is a gelato truck on the laneway that has what we considered the best ice cream ever -- better than the stuff in Argentina, even. Super creamy, bold flavours... we loved it... especially at 40 cents a double-scoop cone!
We stayed at the Sheraton, which is actually in a tony area, by Montevideo standards. There is a mall within spitting distance (apparently the "it" mall in Montevideo, although a bit spartan), the food court of which actually served as a good place for a dirt cheap early lunch (wood fired pizzas, traditional sandwiches, etc). It also contained a grocery store where we bought water, and finally a pharmacy (unfortunately needed).
Near the Sheraton, on the main road running along the "back" of the hotel, we ate at a very modern, trendy restaurant that was fantastic. Again, don't recall the name (however, Montevideo is quite small so you can probably figure these out). It was primarily grilled meats/fish, and fancy martinis. I'm sure the concierge at the Sheraton could direct you. It had a very chi-chi crowd, and was expensive by Montevideo standards.... our bill with drinks came to $40 total (everywhere else was below $20).
Enjoy!
Marno