M.F.
Overall, I think the Gymboree experience depends a lot on the teacher, and (mostly) the other moms in the group. I signed up my daughter when she was a baby, and she seemed to enjoy it, though she wasn't exactly blown away by the experience. Personally, I found the class sort of creepy and depressing, as many of the mothers were singing in their kid's faces while forcing them to do the hand motions or whatever, even when their kids clearly were not enjoying themselves. And it was weirder still to watch the kids being dragged around on that big parachute, when at least half of the poor kids were bawling to get off the damn thing.
Gymboree does have some fun classes for toddlers though. My daughter loved the one where they set up sort of a kiddie obstacle course. I think they call it gymnastics, but really it's just kids playing on fun, safe, indoor climbing equipment, mats, tunnels, balance beams, etc. We signed up for that one at least twice, and I'd recommend it. At least during the winter months.
As for "outdoor activities" with a 13 month old, I think going for a walk almost anywhere is really fun and educational at that age-- especially if you have no particular destination, you aren't in a hurry, and you let the child lead the way. I used to ask my daughter, "Would you like to take me for a walk?" and she'd go nuts with excitement. It's SO rare that kids that age get to feel "in charge" in the real world, and it makes them feel really important when YOU follow THEM. The park is an obvious choice, but even city streets are incredibly interesting for a little person. And they inevitably call your attention to things you never would have noticed -- which is the coolest part. And bring along a bag or a box to collect things (leaves, rocks, sticks, acorns, whatever he likes).
On colder days, letting them wander around museums is great too. (A bit pricey in some cities, I know, but here in DC, we are fortunate to have the Smithsonian). It doesn't really matter if they "understand" where they are or what they're seeing. They love the space, and on weekday mornings most museums aren't crowded (if you avoid the tourist seasons).