Local resident here:
Gastown is a tourist primary area that is safe. warning though, even a block away you will find some very sad things (Not necessarily dangerous, but sad and may make you feel unsafe).
Water Street from Cordova to Carrall, Carrall st from Water to Cordova, and Alexander St. from Carrall to Main St. are considered part of Gastown. No problems other than crowds and touristy stuff.
E hasting St (2 streets over from Water) is the main area of what is called the "Downtown east side", and is has a lot of homeless and people struggling with addiction and mental illness. During the daytime it is sad, and unfortunate. At night it has a rougher feel (but more in the sense of you may get yelled at or see some stuff).
Chinatown is E Pender st (one more past E Hastings) between Carrall and Gore Ave. During the day it is a very interesting cultural area, and I do recommend visiting if you haven't been to one before (eg: San Francisco). The Dr. Sun Yat-sen garden is really nice. At nights, consider this area part of the Downtown East Side (see above).
The Delta Hotel (Vancouver Downtown Suites) is just fine. It is located on E Hastngs, but before it changes to the Downtown East Side (that happens around Cambie/Abbott St), and is only a block away from the beginning of Water street. If you are in that area, walk up Richards to Dunsmuir and try Ramen Gojiro. Very good Tsukamen style ramen.
One note for people who are not local. Downtown Vancouver is a hill, with the peaks at Granville @ Georgia and Nelson @ Burrard It isn't that bad, but be aware of it.
For good waterfront restaurants (I highly recommend doing this):
- Tap & Barrel (Convention center) has a great outdoor patio if it is nice out, with harbour views
- Steamworks (Gastown) has a lower level with great harbour views)
- Carderos (A bit of a walk, but worth it), on the water, amazing seafood, even better views of the harbour
- Top of Vancouver. Pricy, but unparralled views of the area from a 360 degree rotation restaurant.
If you are renting a car, and are on the North Shore (Grouse Mountain, Capilano Suspension Bridge), I recommend "Salmon House on the Hill". It is a high end seafood restaurant in the middle of a residential area with a panoramic view over all of Vancouver. Note: Only go on a clear day. (Well, the food is really good, but the view makes the trip)