I think this is a fascinating topic.
rainbow, I don't think what you did is particularly wrong, it's not like you left them a note in their mailbox, rang the doorbell, looked in the windows, parked outside and watched for hours, etc.

Your therapist is not a robot or a computer, and neither are you. He/she is a regular person just like you and me and you have to make a personal connection. It's very easy to become curious about them, especially if you've been working with them for a very long time. It seems so unfair, doesn't it? They know every last detail about you, and you know next to nothing about them. And especially if you really like them as a person—someone you could see yourself becoming acquainted with if they were never your doctor—it's natural to want to learn more about them. But as long as you can control that curiosity and don't cross that boundary, it's fine. Is your curiosity satisfied by doing it just this one time? If it is, I wouldn't worry about it. But what if it isn't and you start to obsess over it? Maybe it starts to bother you how she has such a nice house/she sure seems happy/she must have major coin, etc.? Then that can hinder your progress and you should terminate (just my opinion, obviously I don't know you or your whole story). You really should tell her, though, since this does involve physically approaching her outside of therapy even though you had no intention of taking the excursion any further. She may not like it...maybe she had something happen to her from a patient in the past. These people have to work with some pretty fragile people (not suggesting you are) and who knows what can happen sometimes. She may have a young family she wants to protect.
Once every few months or so, my therapist will self-disclose something if she sees it as something relevant or helpful to what we're talking about. If she starts going there, I sometimes tell her she doesn't have to disclose anything, it's none of my business...while of course on the inside, I'm thinking "YES something else to learn about her!" LOL But she responds, "thank you, I appreciate that but it's OK".
As far as my own personal "investigations" into my therapist, it has been three things:
1) I have to look up her address/phone number sometimes, and it's on a website of a professional group of behavioral health therapists that has her picture, qualifications, where she went to school, her treatment approaches (which styles - cognitive-behavioral, psychodynamic etc.) I find it comforting to me to make a connection in that way.
2) Once many years ago, she called my cell phone telling me she was home sick and had to cancel our visit (she did not sound well at all). It was a number I did not recognize. My curiosity got the better of me and I looked to see which town the exchange was from (the first 3 digits).
3) I was taking a few psychology classes in college (again, many years ago) and had access to pretty much any article in any journal that I wanted to look up. I had to do it for class...we had to write papers and summaries about a couple different ones. Of course, I did a search for her to see what kind of articles she wrote, but I absolutely never thought of doing a paper on one of hers, #1 it would be strange and a boundary violation and #2 none of them were relevant to what I had to look up anyway. I also did the same searches on all the other therapists I had seen in the past. They are all pretty boring articles, full of equations and statistics and you learn nothing personally about the authors anyway.
I also have had 3 situations where our personal lives crossed into our relationship, all things out of our control:
1) One time, she left me a voicemail saying she wasn't feeling well and needed to cancel. I didn't get it because my cell service was particularly bad that day. So I showed up, and she happened to be there because she had to get her mail or something. She wasn't wearing work clothes and I felt really bad about it, like I wasn't supposed to be there. She told me she left a message and I explained what must have happened. Then she told me she could see me for a half-hour (which was above and beyond generous) but we would have to wrap it up then. Again, I felt really embarrassed for a while after but never brought it up...she didn't either. I should tell you that I have social phobia so any encounters "out of the ordinary" like this are very anxiety-provoking for me.
2) After a visit I discovered I locked my keys in the car, along with my phone inside. LOL, I died a little inside because I knew I was going to have to ask her to use her phone, I had to get back to school and there was nowhere nearby that would have a pay phone without a considerable walk. There were houses nearby, but I do not feel comfortable at all going to someone's house to ask to use their phone. I reasoned that at least I knew her. So I trudged back into her building and told her I was back and asked if I could use the phone. She gave me her cell phone to use, and to leave it on the table when I was done because she had to get ready for another client. It was so weird!
3) Around this time 5 years ago, I mentioned that I was going to see U2 and she said, "me too." This is dorky, but I was really hoping I would not run into her there...of course I didn't, it's an arena of almost 19,000 people. The next visit after the concert, we talked about the show and she asked me if I had a good time and brought up different things that happened during the songs, and what did I think of that. Haha, it was like we were there together but not really, of course.
I think if I was ever to pass her in public and we made eye contact, I would wink at her and that would be it...that's good enough for me. I would never come up to her or anything.
This has inspired me to tell my T all of this...I should walk the walk too. I think I will show her this post...because I obviously haven't forgotten any of this stuff, and I've been having a lot of breakthroughs recently in being a lot more honest about things...not outright lying to her, but by omitting things because I was just not ready to talk about them. Thanks for posting this topic.
EDIT: I just remembered something else. Early in our relationship, I had a dream I was in her house and it was really decked out, marble pillars and gold on the walls, LOL. It freaked me out and I told her about it. I said that I "wasn't obsessed with her" and she said she understood completely what I was feeling, and that it was a just a dream...so it was out of my control. I can't remember exactly what her interpretation of it was, but I think it had something to do with the fact that I wanted to feel safe somewhere with someone taking care of me.