Hotels in Vancouver are expensive due not enough hotels being built because of the crazy property prices and limited develop areas in downtown Vancouver. The alternative is an Airbnb but you have to be careful because a lot of building stratas are making them illegal now but owners still try to stealthily rent their units out. Keep in mind, that the US dollar has like a 33% bonus on the Canadian peso.
Location-wise, the downtown peninsula is the most convenient but it's going to be the most expensive. The main areas to avoid is the downtown eastside along Hastings Street between Cambie and Main. The fringes around it are also a bit sketchy but personally, I feel safe walking around there if necessary. The area also borders tourist areas like Gastown and Chinatown.
If you have a car, a few more options open up just outside the downtown core like around Broadway/Fairview Heights area. Parking costs downtown is expensive of course. Without a car, the best alternative locations are likely just outside of Vancouver proper in the neighbouring burbs Richmond (where the airport is located) by an airport hotel along the skytrain/metro line, Burnaby along the Skytrain line (eg. Executive Suites), or North Vancouver by the seabus (eg Pinnacle Hotel). I don't think it's worth staying out further than that (like in Surrey).
I'm sure you can pull up a list of attractions via google but here are some of my comments around some of the common ones and a few unique ones.
Granville Island: One of my favourite places. It's anchored by a food market building but there are eateries, cool places to shop, etc. It's located on the inlet with great views. There's a great fish & chip place just off the island called Go Fish.
Stanley Park: Various areas to visit: Aquarium, miniature rail, rose garden, etc. Not sure if I'd recommend walking around the park along the seawall (though we've done it) but biking it might be a better option.
Seawall Walk: Vancouver has an extensive seawall. You can essentially walk from UBC to Canada Place along it which takes you past sites such as Vanier Park, Granville Island, Olympic Village, Science World. Great walk during a nice day in the summer. A shorter walk is from Stanley Park/Coal Harbour to Canada Place (where the cruise ships dock). Great view of North Vancouver. You also walk past/near Jack Poole Plaza where the Olympic Games torch is. It's only lit for special occasions though. We do a bit of a circuit along the seawall and along Robson Street and a side trip along Denman to English Bay.
Capilano Suspension Bridge: We haven't gone in years but we got a recent report from some relatives. It's not as tourist trappy as before (eg. There's a free Lynn Canyon Suspension Bridge) as they've actually built out the area with additional attractions/walks. There's a free shuttle from Canada Place.
Grouse Mountain: Similarly, haven't gone in many years. It's kind of a pricey ride up to see the attractions. You can also hike the grouse grind up.
Gastown: Gastown is ok for a quick visit. People like the cobblestone streets, take pics of the steamclock, take pics of the statue of Gassy Jack. It's pretty touristy but there are some interesting places to eat and a bit of a pub scene.
Chinatown: Chinatown is a shadow of its former self as a lot of the commerce has decentralized and moved out into the neighbourhoods and suburbs. One of the main attractions is the Sun Yat Sen Gardens which is nice. (note, there's a park area outside the paid garden area.) Some new and interesting eateries (not-necessarily chinese) have been popping up in the area. We occasionally pop into New Town Bakery to get some pastries.
Flyover Canada: It's kind of a disney-esque ride at Canada Place where your seats lift off the ground and you kind of fly around different panoramic videos of the Canadian landscape. My coworkers went there recently for a team building event. I enjoyed it but it's of pricey for what it is.
Shipyards Night Market: During Friday nights in the summer, there's a night market across the harbour beside Lonsdale Quay. Easily accessible via the seabus. There's entertainment, food carts, a great view of downtown Vancouver.
Richmond Night Market: During weekend nights in the summer, there's also a night market by the casino in Richmond. Accessible by skytrain. I don't love this one as much because the stuff they sell there is tacky (cell phone accessories, socks, etc) but they have a bunch of food stalls which is kind of fun.
Food carts: Lots of food carts around downtown Vancouver, though mainly during the weekdays. Favs: Tacofino, WakWak Burger, Le Tigre if they ever get their truck fixed, Mogu.
UBC/Anthropology Museum: It's a nice walk around the UBC campus. People go to visit the Anthropology Museum. I haven't gone in years but I'm not a huge fan of west coast native art.
Queen Elizabeth Park/Blodel Conservatory: Nice gardens. Easy to get to via skytrain. But likely on the B list unless you really like gardens. Nice views though as it's the highest point in Vancouver proper.
VanDusen Gardens: Ditto.
