My ex and I are starting visitation again after about a year, and we've set up a schedule of visits twice each month. A couple weeks ago, DD and I met him at a kid cafe/toy store near our home because it had a play area. During the visit, he just watched DD play and told me he was very nervous and didn't know what to do; he didn't interact with her much. Afterward, he told me in an email that the kid cafe was too distracting for DD (who is almost 2), and that we should pick another place. We're meeting at the park this weekend, but it looks like it might rain, so it would be good to have some alternatives. It's a little frustrating, though, because any place that DD finds interesting, X calls distracting, and when I try to keep DD's attention on X (for example by keeping her at the table where he and I are sitting), she fusses because she doesn't have enough of a relationship with him to want to interact with him.
Suggestions for a neutral place (not either person's home) to meet?
Some ideas I had:
Family study room at the university library (but it has toys, so DD might be too distracted)
Going to the park anyway, with jackets and DD's umbrella
Indoor pool at the gym (but DD is partially afraid of water, and X doesn't read her signals well, so he might freak out when she freaks out when he tries to take her deeper than the steps into the pool. I'm not sure if telling him to stay on the steps would help)
Local kids' museum (also probably distracting)