Given the denominations you list - Unitarian Universalist, Episcopalian, UCC - it seems pretty clear that your interests lie on the “liberal” end of the denominational continuum. IME there are far fewer of this type of congregation around than more mainline protestant churches. So your choices will be significantly limited geographically. There will probably only be 1 or 2 or each denomination that are within realistic distance for you.
One thing I’ll point out is you need to decide whether a required belief in a particular God is a deal breaker for you. If you believe in God and prefer to church with fellow believers, well, you might rule out UU. If you are open to “spirituality” absent belief in the supernatural, UU may be your best choice.
IME, there is a lot of benefit to attending a logistically convenient church, especially if you are going to be hauling kids to RE calsses and activities. There are also benefits to attending a “community” church: you are more likely to see fellow members elsewhere than in church, it will be convenient to stop by for reasons other than sunday sermons, etc.
Get info on what the kids’ RE program involves, and seriously plan out the time committment you wish to make. For example, we found it best when church had kids’ RE at the same time as the service we wanted to attend. At times when our kids attended RE at 2 different times, or later in the afternoon, it was much more of a hassle to have to drive 20 minutes for every obligation.
I would recommend researching the nearest congregations on-line. It is quite common for churches to post recent sermons, calendars, groups and committees, classes, etc. Then you and your husband can either attend singly, or get a babysitter and attend together. I’d just go and sit in the back. Personally, I probably would not wear a visitor name tag - but if you do, that is proably a good guarantee that some friendly sort will talk you up after services.
UU churches - and I believe many others - have coffee between services, where you will be able to ask questions of members. And realize that the makeup of different services may vary. Generally, the earlier services are attended by older folks.
Disclosure - My wife and I were raised catholic and lutheran, and have attended UU churches for the past 15 years or so.
We are in the unfortunate situation of being equidistant between 2 UU churches. So both require 15-20 minute drive, and neither qualify as a “neighborhood” church.
IMO, UU churches generally have excellent kid’s RE programs - tho some aspects of them have been controversial. They do more “comparative religion” studies than most christian churches, and offer “quasi-sex ed” for older kids. Undoubtedly not everyone’s cup of tea.