I think you should try to schedule a visit to OSU. Do you have some vacation days to take? You might have to pay for it out of pocket, which isn't great, but at least you do have a job. And, like you said, you want to make sure you are going to be happy there since you'll be there for 5 years.
I suggest visiting because to me, it sounds like the biggest worries you have are about department/research fit and lifestyle/culture fit. Both of these things can only be resolved with a visit! It's easy to get a lot of misconceptions about how things are at a place from your own impressions or online research. Nothing can really replace an in-person visit.
As for transferring, I think the term "transfer" is a bit of a misnomer. What you would be doing is leaving your OSU program and applying for a new one. You will likely start over again. You might be able to get a MS in Physics from OSU if you leave early. So typically, you would go to OSU for the first year, and then in your 2nd year, if you decide to leave, you would apply again. You will need to work hard in your first year to get very strong letters from OSU. You'll be at a disadvantage compared to students who have not started a PhD program, but this can be mitigated if 1) your letters from OSU show that the reason you are leaving is either personal or research fit, not performance related and 2) if you improve your application a lot by doing some awesome work at OSU. So, to get both of these, you'll need to work really hard.
That is, "transferring" is basically equivalent to doing a Masters and applying again. The difference is that you get to start this fall and you might want to just stay at OSU if you find that you actually like it. I think it's dishonest to accept a funded PhD offer with the intention right off the bat to leave after a year or two. However, it's completely fair to accept an offer with the intention of re-evaluating whether or not you are happy in this PhD program after a year. As long as you are still open to the idea of staying, I think it's okay to take the funded offer.
Finally, 26 isn't that old
Yes, you will be older than grad students entering right out of undergrad, but in the long run, it will not make a big difference. When people talk about discrimination against older applicants (for grad school, postdocs, faculty jobs etc.) they are usually talking about much older people (i.e. starting a grad program in late 30s or 40s). But I do understand that maybe you're getting to the age where you don't really want to live the "grad student lifestyle" and want more stability in life. I'm going to defend very soon (just before I turn 30) and I'm really looking forward to being a "real person" instead of a student