Cold side of Lake Anna is about 10,000 acres big. That's a LOT of ground to cover! While Tox is more familiar with the "honey holes" I'll suggest you try areas like Rose Valley, the Splits and down by the dikes. Also try the docks near Sturgeon Creek. Since there is very little vegetation (at least that I've been able to find!), artificial structures like the dikes, docks and drop offs seem to be the best bet.
For tubing, if you go down lake from Anna Point Marina, past Sturgeon Creek, there is a cluster of islands on the left. Nice back coves for some tubing or just anchoring to swim without fighting the wakes from the inevitable summer boat traffic.
Oh - and be careful!! Lake Anna's cold side is an unrestricted HP, publicly accessible water body meaning lots of jet skiers, big boats, bass boats, wakeboarding boats, pontoons, deck boats, etc. all mixed together. Not everyone is as familiar with proper watercraft operation and the rules of the water as they should be. That and residents of DC seem to have "discovered" the lake. Its popularity is growing.