I live a couple of blocks from the Sylvia. You will be in prime walking territory. Here’s some suggestions (some echo what others have already said)
1. The seawall is across the street from your hotel. When you are looking at the water, English Bay, turn left to take the seawall to Yaletown and right to take the seawall to Stanley Park. It’s a 10km (6 mile) walk around the entire park on the seawall. There’s lots of nice forested trails in the park, a rose garden, an aquarium and a few restaurants. The hotel will probably have maps available. There’s a brewpub/restaurant in the park a short walk from the Sylvia that has a nice deck.
2. Granville Island: if you head left from your hotel you’ll see a foot passenger ferry terminal just before you walk under Burrard Street Bridge. There’s another (separate company) ferry past the bridge. Take either of these to Granville Island. I’d get a day pass and cruise False Creek. You can get off at various stops, have lunch, wander around, catch the ferry again or walk to the next stop. They have good maps and the ferries run frequently. Granville Island will be very busy but you can wander around and look at boats, art and craft stuff, and have lunch somewhere with a view. Whale watching tours leave from Granville Island.
3.Canada Place is the central place for tours as it is also the cruise ship terminal. You can walk there easily by walking down Denman to the Coal Harbour seawall and then taking the seawall to Canada Place. You can also enjoy watching the seaplanes land and depart from the terminal on the seawall. You can book a seaplane tour at the terminal.
3. Gastown: I would not bother.
4.Downtown is immediately south of the Canada Place. The usual shopping, restaurants, Bill Reid Gallery is worth a visit, I don’t know what’s on at the Art Gallery right now
4. Shipyards District North Van. You can take the Seabus (part of our transit system) to North Van from Waterfront Station which is very close to Canada Place. When you get off there’s a big public market area and the Shipyards district which is an old shipyard that has been converted to fancy condos and an arts and culture hub. Nice to walk around, get lunch, see Vancouver from across Burrard Inlet. There’s a bit of craft beer district there, if that’s of interest. Also a small art gallery focused on photography. It’s a great building to look at even if you don’t go in. Admission by donation.
5. Restaurants. Denman Street is block from the Sylvia and is basically all small restaurants that serve the neighbourhood and those who come down to the beach at English Bay. There’s a huge variety, the restaurants are small and casual. Lots of variety- Japanese, Korean, pizza, tacos, Greek, Middle Eastern, etc, etc. For a more upscale restaurant on a leafy street off the Main Street, you could check out Robba da Matti on Haro Street. Again a short walk from the Sylvia. It’s Italian, has a patio and is popular so make a reservation. Also Tavola on Robson but it is very noisy. Espana on Denman is Spanish and a bit more upscale, but casual (Vancouver is casual).. I like Nook for pizza and casual Italian. No reservations and very popular so go early or late. There’s a ton of Asian restaurants on Robson around Denman if that’s of interest.
6. Practical There’s a drugstore (London Drugs) on Davie a few blocks from the the hotel. Also a Safeway for groceries and a liquor store (no wine, beer or liquor sold in grocery stores here). Your hotel is in a residential neighbourhood so all the essentials are at your doorstep.
Someone mentioned the Museum of Anthropology at UBC. It’s fantastic but unfortunately closed for a big seismic upgrade.
Enjoy your visit!