Another vote for riverside. I don't like living in East Providence but it's better than Portsmouth. Being close to Newport isn't really that attractive. It's over-hyped.

I lived in Bristol which is just over the bridge and it was a pain in the ass to get anywhere.

I take dogs out a lot in that area and you have lots of choices. Rose Larrissa Park has shoreline access. Haines park has wooded areas for exploring by the boat launch. There are some walking paths in the woods by Kettle Point that connect to the bike path.