I would have to say that the best places for walking/running/hiking are as follows: Stanley Park, Lynn Canyon, Grouse Mountain, Jericho Beach and Lighthouse Park.
If one is interested in shopping or overpriced (my opinion) food then there are plenty of good shops and restaurants on Robson Street. My personal favourites would have to be Zefferelli's (Italian) and Ebisu (Japanese).
For entertainment, I'd recommend the Vancouver Sports Theatre down on Granville Island. There are also plenty of unique restaurants both near the Island and on the island itself. It is also worth looking at the Emily Carr Institute and the various artistic shops down there.
Last but not least, I'd recommend that people avoid going to either Grouse Mountain or the Capilano Bridge if they are simply looking to get a good view from these tourist attractions as they are both rather pricey.