Nikon 35mm f/1.8G AF-S DX lens is it good?

Is the 35mm f/1.8 a good lens as my first secondary lens for my entry level D3100? I travel and mostly take pictures outdoors, scenarios, animals, nature, buildings and outdoors, if that helps.

No - it isn't good for that. The 35mm would be good for low light street and indoor photography.

It isn't wide enough for buildings and is limited for landscapes - a 10-22 wide angle zoom would be better.
It isn't long enough for animals - something in the range 70-200 or 300 would be better.

Assuming you already have an 18-55 kit lens then go for a 55-200 or 250 zoom as your next lens

I had that lens for awhile, but did not like it vs. The 50mm f/1.8. The reason; the 35mm has a bit of perspective distortion vs. The 50mm f/1.8, and I have no problem in backing up a bit to compensate for the crop factor.

While perspective distortion is not very significant at 35mm, it's there. And having both lenses meant I would usually chose the 50mm over the 35mm every time I went out shooting photos, so the 35mm usually sit in the closet.

Even with the crop factor, I still prefer the 50mm lens over the 35mm.