Further to the above:
One thing to keep in mind about the weather in BC is that by the end of Aug. or early Sept., the eastern and northern part of the province is starting to get cold and places are starting to shut down for the winter. Might be better to time a trip so that you end up in the south coast area in later August. We typically get decent weather into late Oct.
Another thing to consider is that gas prices have shot up lately to about $6 per gallon. If you happen to be near the US border, you can get gas at around 1/3 less.
On things to visit, you might find the Sunshine Coast nice. It's a short ferry ride from just north of Vancouver. If you travel north up the Sunshine Coast and get to Powell River, you can take a ferry over to Comox on Vancouver Island. From there, you can drive down to Victoria. Victoria is lovely and they say it is more British than the British. Be aware that ferry fares on BC Ferries is expensive. One way to the Island for our 50' truck and trailer is about $400. They have had discount fares or 1/3 off on Tuesdays and Thursdays lately. I recommend getting reservations ahead of time as the ferries are quite busy in the summer.
BC FerriesThe west coast of the Island, Tofino and Ucluelet is interesting and is where world famous Long Beach is. You'd also drive through Cathedral Grove, part way between Port Alberni and Parksville, on the way to Tofino. Cathedral Grove is a protected old growth forest in a provincial park. Port Alberni has an annual salmon festival Aug. 30 - Sept. 2.
If you have the time, you could take a ferry from Victoria to Port Angeles on the Olympic Peninsula in the US. From there, you could take a ferry from Port Townsend to Anacortes, just south of the Canada/Us border. Personally, I would highly recommend this.
Another suggestion would be heading north out of Vancouver and driving up the sea-to-sky highway to Whistler. From there, you can drive north and then down to Lytton and the Frae Canyon or you can head over to Kamloops. Kamloops has the only genuine desert terrain in Canada.
Barkerville near Williams Lake is interesting. It's an old mining town. Nelson is also interesting and is a historic town with numerous old buildings. Harrison Mills in the Fraser Valley is another interesting place.
If horses interest you, there are tons of places around the interior of the province where you can find horse rides. There are also dude and guest ranches around the province and you could possibly park your RV for a day or two and stay at one. We went on a horse ride at a guest ranch near 108 Mile House a few years back and it was fantastic.
Unless you really must, I would avoid going into Vancouver and adjacent areas (Richmond, Surrey, etc.) because it's so congested and slow to get around. If you do want to go into Vancouver though, consider a visit to Stanley Park which is allegedly the largest urban park in North America.