It's bikeable, with a few tips in mind:

• Going up College Hill (heading east on Waterman, for example, or any of the east-west streets between Olney and Wickenden) is steep. Some people can do it, but I end up walking my bike up or by riding along the river on South Water Street to Wickenden and then taking Benefit, Hope, or Brook north if I have the time.
• Drivers will not look out their side view mirror before they open their doors, so be alert if you see someone in a car. You run the risk of getting doored.

Since you mention a scooter, I'll also note that some of our sidewalks are made of brick (around our beautiful statehouse, and along Benefit Street, for example). They are not fun on a scooter. The Benefit Street sidewalks are also quite bumpy due to tree roots and missing some bricks, so proceed with caution. That said, you can ride on the street there fairly comfortably.

Finally, GF: Some have mentioned Indian restaurants. I also recommend Wildflour and the Garden Grille, but next door to them is Rasoi, which is very GF-friendly. Their sibling restaurant, Kabob and Curry, is on Thayer Street, so if you want to shake things up location-wise, that's a good rec.

To be honest, though, Providence is pretty small, so walking actually works even better, with the exception of heading to Garden Grille, which is further from downtown. (RIPTA services the area fairly frequently, and is another option.) For example, walking from Providence Public Library (the western edge of downtown) to Thayer Street takes about 23 minutes. Starting from Federal Hill adds another 10 minutes.

Happy travels!