I've eaten solo almost everywhere, from Signature dining to family/interactive spots. With exception of the popular bars, and Biergarden, I've always gotten my own table.
At 50s Prime Time, Whispering Canyon, and Skipper's Canteen, there was still interaction with wait staff - often they'll do the schtick on you in a way that includes nearby tables - like 'he didn't eat all of his green beans!'. Or if I wasn't looking for the full interaction, I just made a hint of it early on and the CMs take the clues very well and will play it down.
Last trip, I did Steakhouse 71, Topolino's,
Geo 82, Prime Time, Trattoria Al Forno, Nomad Lounge, Cake Bake Shop solo. I prefer to get tables, not bar seating - more room to spread out, relax - tables are close enough that if you feel like engaging or talking with others, you can - but unlike the bar, you're not shoved right up against others (fine when they are social and you wan tto talk too - but awkward if you get a party next to you that clearly doesn't want to be social).
My December trip upcoming is likely to be solo (a friend is considering trying to make it, but probably won't be able to swing it) - I've got T-Rex, Beak & Barrell, Art Smith's Homecomin, Boatright's, and Frontera Cocina booked.
In February, I'll be with a friend and doing two, and in June will be there with another friend...September next year may be solo, then December with a large group - my trips are random mixes of solo, one friend, some family, or big groups.
As long as you don't have any hang-ups about eating solo, don't worry about it and choose anyplace you want to try or eat at - there are only 3 or 4 restaurants/bars where they may seat you with others - 99% of them you'll have your own table.