I would try to stay away from staying in Richmond just because you’ll be drive 20 to 30 mins or so to get anywhere in Vancouver depending on traffic (and dealing with bridge traffic). Richmond is not very dense and not too interesting for the average tourist (although it does have some highlights)

Briefly searching Priceline.com there are some hotels in the core or close to the downtown core in your price range. Because you have a car, I wouldn’t say it’s essential to stay in the core.

Stanley Park is a must (although you’ll be there because of the Aquarium anyways). Biking, rollerblading or walking the seawall is quite fun too. The wall actually extends quite far around the city, so you can just pick one part to do.

If you’re into nature I’d suggest Lynn Canyon (avoid the pricey Capilano bridge, unless you have money to burn. It’s not not worth going, but it is quite pricey). There are some trails there that are just flat walks.

If you’re into boutique shops, independent designers, and antique shops, I’d suggest checking out South Main street. Between 12th street and 25th ish.

I personally like Jerico beach (western part), but not necessarily because it’s the ‘best’, but because it tends to be less busy and there’s skimboarding.