DJSchiff

Not weird to ask at all, and congrats on coming out! I'm a trans woman and also considered how receptive various universities would be. One thing I did was look up how active the campus LGBTQ groups were, and if there was any support for trans grad students too.
Regarding healthcare, it's going to vary depending on both University and State statutes/laws. It's definitely a good thing to look up before attending, and if you have any questions feel free to pm me

I don't know of any places to "avoid", but I would recommend checking out what resources are available at every school you get accepted to.
For example, is there a gender and sexuality center? Are there trans-friendly organizations where you can find social support? Are gender-neutral bathrooms accessible? Are there any counselors/psychologists at the mental health center that specialize in LGBT issues? Do some of the doctors at student health have experience working with trans* patients? There might be other factors that are important to you too.