MY KLAXON!
Besides the spots mentioned above. I'd add for trout: Whiteoak in SNP, the Moormans (only 30 min or so from town although there's a bit of a hike to the good water; it's a very popular stream-stocked water below the dam, brookie water above although you need to go past the third stream crossing to get to good water), and in addition to SNP bluelining, GWNF/TJNF bluelining. I feel like eastern slope streams get marginally less pressure than western slope streams. RE: the North, you don't even need 4WD, my Prius got up to the brookie water there fine.
For bass/other warmwater: the Rivanna has some good smallmouth water around where 29 crosses and maybe by Riverview Park although it's not good wading. I've also heard good things about the Maury around Goshen Pass (bit of a drive but there you go) and the James by Peaks of Otter although that's kind of pushing "Charlottesville area"