rare to see anyone posting on here from hampton/tidewater area so I made an account just to tell you.
Minus the brackish water, and thus, the jellyfish at times, the warwick river is incredible. I mean incredible. On a weekday you will find 2 or 3 boats at max out there and weekends 5-10. This river is surrounded by tall marsh grass which acts as a wake dampener - no rebounds off those silly headwalls in lakes. Also, it snakes and winds so you are guaranteed to find glass, yes - glass, on even the windiest of days (40mph). Speaking of snakes there are occasionally mokasins so just fyi. Another badass thing about this river its that it is right next to Fort Eustis base. I know you mentioned being in military so this may be less of an appeal, but blackhawks, chinooks, and other sweet helicopters fly just over head regularly it makes for pretty epic scenery.
Getting there: drive to the end of Denbeigh blvd and you will find Denbeigh docks - left takes you out to the james - right takes you into warwick.
Further up the james are some good spots as well. I suggest putting in at Jamestown settlement, then cruising up to whats called College creek - there is a little beach there and you drive under the parkway.
As others have mentioned, Chickahomony is incredible. Only issue there is its not very post-work accessible. Roughly and hour or so from hampton.
Lake Gaston is good on weekdays and if it is not windy and if you know the right coves. Don't get me wrong, I have family that lives there, we have a house there, but as far as water quality and boat traffic goes, the Chickahomony and Warwick are far superior... If you are looking for a lesson (even if you think you are really good - he trains other pros actually) go see Adam - he really is a super nice and helpful dude.
Hope this helps - enjoy hampton