Hi,
First of all, welcome to Vancouver.
There are many cheap places to stay. I would recommend Hostelling International - Vancouver Central and Hostelling International - Vancouver Downtown.
http://www.hihostels.ca/hostels/BC/BCRegion/VancouverDowntown/Hostels/
They offer both private rooms (for about $50) or shared dorm rooms (for about $25). The great thing about staying at hostels is that you get to meet travellers from around the world. You may also want to try YWCA as well.
Here are places that I think all visitors should visit:
If you are staying in Vancouver for a week, then I would choose the following attractions:
- Granville Island: public market, improv shows, artist workshops (approx. 1/2 day of exploring)
- Stanley Park: Aquarium, mini-train, Sea Wall (1/2 day)
- Lynn Canyon Suspension Bridge (free) or Capilano Suspension Bridge (admission required) (1/2 day - 3/4 day)
- Canada Place: CN IMAX theatre and the 5 sails (1/3 day)
- Robson St: shopping and dining (Downtown)
- Granville Entertainment District: lots of clubs and pubs, few theatres, Sears, The Bay, Winners, Future Shop, Tom Lee Music, etc. (Downtown)
- Central Branch Library (Downtown)
- Gastown: historic Vancouver, dining & clubbing (Downtown)
- Chinatown: Dr. Sun Yat Sen Garden, World's narrowest building, (1/3 day)
- Vancouver Art Gallery & UBC Robson Square (souvenirs) (Downtown)
- Vancouver Museum & Vancouver Maritime Museum (1/2 day)
- UBC: Museum of Anthropology, Wreck Beach (clothing optional), Japanese Garden, etc. (1/2 day)
- Queen Elizabeth Park and Blodel Conservatory (1/2 day)
I personally like to visit neighbourhoods because they are unique to each city:
- Chinatown
- Main & 49th: Punjabi Market
- Commercial Drive: Little Italy & "Hippie" vibes
- Davie Village & Denman: GLBT community
- Kitsilano: West 4th Ave. for sports stuff like snowboards, skiis, etc.
- Upper Granville: Granville & Broadway: mid to upscale shops like Caban, Restoration Hardware
- Broadway & Cambie: outdoor gears shopping with Moutain Equipment Co-Op, Taiga Works < popular & competitively-priced outdoor clothing, and many others
If you have time, at least a day, then Victoria. Have another free day? Then, consider Whistler for skiing and snowboarding.
In terms of shopping, I would recommend:
- Souvenirs at Gastown
- Clothing and Apparel at Robson Street, Pacific Centre, and Metropolis at Metrotown (largest shopping complex in BC)
- CDs and DVDs at Future Shop, Best Buy, and A&B Sound
To plan your visit, you may want to visit:
http://www.tourismvancouver.com/
http://www.vancouver.ca
http://translink.bc.ca (public transit)