Supposedly the shortest, easiest way is to take I10 all the way to LA and hop on the 5 up to your place. If you were in Portland instead, there's a diagonal route through the snow and mountains though
I haven't been to Florida since I was 6, and I haven't been to Dallas since I was 2. But New Mexico and Arizona, I've been there much more recently! And the Texas Panhandle, but that's not worth mentioning lol.
I don't know the deep south at all, so unless you want to see some civil war battle fields, I'd stick to 10 till around El Paso
. Cutting through NM to the 4 corners area is very nice - warm mountains and not many people if you stick to state highways - I once drove along US54 from I40 in north central New Mexico to Alamogordo and didn't see more than 10 vehicles till I was almost to the city! Chaco Canyon in NM is very cool, but would be almost imposible to get to in a Locost. Mesa Verde is worth the visit. Almost every national park is worth it around there if you think ancient pueblo dwellings are interesting.
5 and CA-99 are both pretty boring through the central valley too. But once your around Fresno, you can take some mountain roads that top out at ~3000' (CA-41, 49, 120) and they shouldn't be any snow, and you'd stay in some nice country till just north of sacramento.