There are many places of interest and beautiful walking trails on the lower mainland. However, I picked a few based on the sheer quantity of caches. You mentioned that you don't want to drive so once you hit these spots you can basically park and stroll.
1) Stanley Park -- doesn't have a high concentration of geocaches for a park so close to the city centre but a walk around the seawall is a must for a first time tourist. Lots of pretty vistas, history, art and perhaps the best view of downtown on a nice day.
2) Pacific Spirit Park / UBC -- home to British Columbia's oldest cache and the infamous Wreck Beach. I don't think you'll see many nudists in November, however. After finding a few caches the Museum of Anthropology is a great place to see West Coast native art.
3) Iona Island -- There is a beautiful walk on one or both spits out into the ocean. You're actually walking on the pipeline that takes Vancouver's sewer water out to the ocean. This is a sunny day low wind walk. If it's windy or rainy, forget it. You'll be miserable half way through. There is a high concentration of geocaches and this area offers an walking experience like no other in the Lower Mainland. Once at the end, you really feel like you're in the middle of the ocean.
4) Burnaby Lake -- Take bird seed. Piper Spit is one of the only areas in Vancouver where people are encouraged to feed the birds. And in turn, the birds flock to the area during migration seasons. There is literally a cache every 161 metres around this lake. It'll take a few hours but you'll get 60+ caches to add to your count.
5) Belcarra Regional Park -- There are three power trails in this park. My favourite walk is along the ocean. It's a well maintained trail with some hidden beaches and the remains of squatters shacks. Another high concentration of geocaches. If you take Ioco road you'll pass what is left of the historic company town of Ioco.
6) Bunzen Lake -- This is the closest you'll get to a true BC mountain lake close to the city. Mountains jut out of this lake. There are a few caches within walking distance of several parking lots and if you're feeling adventurous there is a mountain hike around the west side of the lake on the Des Vistas trail.
7) Lynn Creek -- No trip to Vancouver would be complete without visiting the North Shore mountains at least once. Upper Lynn Canyon has a high concentration of geocaches. I've been up as far as "The Amorous Trees" but I've been told the hike gets a lot harder after that. The good thing is it's all downhill on the way back. Mid Lynn Canyon has a cool pedestrian suspension bridge that is worth a visit. Lower Lynn Canyon has fewer caches but there are some cool tunnels carved into the hillsides and the remains of some frontier homes.
8 ) Cypress Mountain -- This park has perhaps the best view of the Vancouver area right to Washington State. This is a clear day cache hike. If you decide to go to Eagle Bluff you will not be disappointed with the view. Bring a snack for the two resident ravens who like to join people for a picnic. Along the way there are miniature mountain lakes dotting the landscape. This is not an easy walk. The trails are maintained but not easy in parts. For this trek, along with any outlying areas in Vancouver, Bear Spray is a good thing to have along.
An honourable mention also goes out to the town of Steveston which has the highest concentration of innovative hides. There are some fun caches there. It may be further than you want to drive, however.
Lighthouse Park (West Vancouver) is also a nice area. Lots of geocaches, an interpretive forest describing native trees and, of course, the historic lighthouse. Lots of geocaches and if you take Marine Drive, it's a very pleasant drive (when there is less traffic) with some fun caches along the way. Marine Drive is most scenic drive from Lighthouse Park to Horseshoe Bay.
I hope this helps.