I'm not very familiar with Canon, but in comparing the Nikon D5100 to the D3200...
The D3200 has a higher resolution (24.2 MP v. 16.1 MP) and slightly better image quality. Megapixels really aren't as important as they used to be, at the beginning of the digital camera, so I wouldn't make that alone my deciding factor. The D3200 is a bit smaller and more lightweight, so it might be easier for you to carry around the parks. Also, it's a bit less expensive.
The D5100 isn't a huge step above the D3200 as far as overall quality and features. It does have the flip-out screen which could be helpful for taking shots low to the ground, or if you plan on self portraiture. It also has a slightly larger sensor and higher ISO capabilities (one f-stop better than 3200) so you have a bit of advantage over the 3200 with handheld low-light shots.
Personally, I think I'd go with the D3200 over the D5100. It's a slightly newer camera body, more lightweight, and slightly less expensive. In my opinion, the 5200 is not much of a jump from the 3200. If looking for a higher-quality camera than the 3200, I would suggest skipping the 5100 entirely and looking at the D7000 (and ideally, the D7100). But, I think the 3200 is the ideal entry-level camera body and probably what you're looking for.
As for walk around lens for the park, I would suggest skipping any sort of bundle and getting the camera body only and spending more money on a nicer lens. Best walk-around lens is of course personal preference, but my favorite (and I think many others on this board like too) is the Tamron f/2.8 17-50mm lens. Generally, I would suggest splurging on a lens with wider aperture capabilities like an a f/2.8 lens. Most kit lenses are f/3.5-5.6 and that won't really affect your ability to take sharp photos in daylight, but a wider aperture is really helpful for low-light handheld photos.
So my suggestion would be to choose the lower-end camera body model, whether Nikon or Canon, and then upgrade the kit lens to an f/2.8 if possible. Also, when looking at lens upgrades, do not feel obligated to stick with Nikon/Canon. There are great lenses from brands like Sigma, Tamron, Tokina that are high-quality but less expensive.
But, as always, it's personal preference. I'm sure there will be someone to disagree with me! Just go with your gut and do what's right for you. Only so much research and debating can be done... then you just have to go for it!