What you get out of a visit to Vancouver really depends on the type of things you’re interested in. The aquarium in Stanley Park is awesome, but Stanley Park itself is kind of unimpressive. Walking on the seawall around the perimeter is actually more interesting.
Granville Island in the summer is fabulous… there’s a reason it’s always packed with tourists! There’s a lot of fresh fruit, seafood and funky jewelry to be had down there. There’s also a small gallery at the Emily Carr Institute with some interesting pieces done by art students.
UBC campus as mentioned upthread can be interesting but they’re always under construction, so it can be confusing to try to find your way around when they’ve changed the roads and blocked off access. It’s best to take the bus down and navigate by foot. If you end up there, don’t miss the Museum of Anthropology. They have fantastic First Nations exhibits and an open storage collection. You can literally spend the whole day pulling open drawers and looking at artifacts. The new(ish) Beaty Biodiversity Museum is kind of cool too, but not very big. Nitobe Gardens in the summer is gorgeous.
The Capilano Suspension Bridge is decent, but it’s not really accessible by transit. Well, it is, but it’s going to take you a long time if you do it by actual public transportation and not a private tour bus. If you end up being in a car, I’d actually recommend going to Lynn Valley for a hike. They also have suspension bridges, but it’s less touristy and free.
I’m a local, so I remain thoroughly unimpressed by the steam clock in Gastown… but tourists from all over seem fascinated by it. There are always a bunch of them blocking up the sidewalk taking pictures! Gastown itself has a bit of charm but it’s changed a lot over the years and doesn’t have much for people to do except eat in the restaurants.
One place I think a lot of tourists miss out on is “downtown” New West. It’s not Vancouver proper so a lot of people tend to dismiss it, but it’s actually older than Vancouver and has maintained a lot of its architectural charm. It’s easily accessible by skytrain (just get off at New West station).
Oh, and one place to avoid is definitely the Museum of Vancouver. I’ve never had anyone visiting who wasn’t disappointed by it. It’s incredibly small and the displays are quite amateurish. It shares the same building as the planetarium… and it’s a small building!!! It really is meant for locals who want to see (sometimes cool) temporary exhibits but provides very little representation of Vancouver itself.
Phew… hope these suggestions give you a start to your plan. I could come back with more suggestions if you indicate what sort of things are your cup of tea.