There isn't anything within a block of the 4Pts (except the restaurants at the hotel, good but not cheap), however a short walk takes you to Darling Harbour and the dozens of tourist-trap restaurants there (some quite good, but generally not cheap). For cheap you need to walk about a mile to chinatown.

The Sydney aquarium (very close to the hotel) is a must-see. Lots of other places in town, 2 days is not enough time to see 1/4 of them.