Really just try to get out there as much as possible and fish in my opinion. By the law of chance you'll get lucky and have some good days.
Rudee is actually a very good place to fish this time of the year early in the season, but you indeed may get hung up a fair bit if fishing from shore at the rocks. I'd try using some cut finger mullet there for puppy drum, and you may get a bluefish on that also. The Narrows I haven't fished in a couple years, but it has produced fish for me a few times in the past. Mostly fished it on my way to and from trips to Seagull pier on the 1st island of the CBBT.
Local piers, despite what you may have read, can produce nice fish for you. Just keep in mind they can get pretty crowded on weekends and during nice weather. Most of the 40+ inch red drum I've caught happened out on a pier.
Other fishing spots to suggest kind of depends on where you live in the area, or how far you're willing to drive. Also what type of fishing spot do you like (like do you prefer fishing from the beach, etc)? Lots of surf fishing on the ocean from Sandbridge to Back Bay. Also some decent surf fishing from Lynnhaven area to Chicks Beach at times, and even further in the Bay towards Ocean View. You also have a few tidal rivers to fish that are connected to the Bay, like the Lafayette River and the Elizabeth River. Both are tidal saltwater rivers, so you can catch some of the same saltwater fish you may catch in the Bay (like puppy drum, striped bass, and a few others). You can fish the Lafayette River from a public fishing platform under the Granby St. bridge. You can fish the Elizabeth from a few public spots, like around the Harbor Park area of Norfolk for example.