I'm surprised nobody answered this question yet.

I was told by a couple of guys that 20-24 mph would be good on the road, but so much depends on traffic conditions. For example, you don't really need to be pedaling frantically, bursting your lungs and all that if traffic volume has forced cars to go only 10 mph or less.

I find that I only need to ride just fast enough to discourage motorists from trying to cut me off in order to park on the side of the street - or at least go a fair distance ahead of me before turning right or parking.

Sounds like riding only on sidewalk is not a choice for you anyway. To build your confidence riding on the road, try riding with a coworker to/from work and/or find a casual cycling group that does fun social rides. You might also find a "city cycling" class offered by a local nonprofit.

As others have said, riding on the sidewalk can be dangerous wherever driveways and roads intersect with the sidewalk. I recently witnessed a cyclist nearly crash into a car that came out of an underground parking garage. The cyclist was pedaling along leisurely, then the car suddenly materialized seemingly out of nowhere because it was so fast. The cyclist saved himself by putting his hands on the car to stop his fall. Even a responsible driver coming out of a driveway might not spot a cyclist on the sidewalk in time because cyclists move faster than pedestrians.

I also recently saw a cyclist lying on the street injured because she was hit by a car turning left, while riding on a crosswalk. So watch out when you ride on a sidewalk and have to cross a street on a crosswalk to get to the sidewalk on the other side.