I’d probably start with a table of contents universe to see what the various options are. Then I’d look for ones with interesting pathogens, like de-aging viruses, and parasites like in that one episode of Futurama (I just wouldn’t be worried if someone loved me because of who the parasites made me into).
Then I’d go visit versions of universes around the present time after I had made various changes in the past to see how it impacted things. The beauty of the multiverse is that I wouldn’t even have to ever do those changes in the first place, another version of me would have taken care of it, so I could just jump to the results. Then I could also check out the ones where I failed but still had an impact, they would probably be interesting.
I’d crash Stephen Hawking’s time traveler party. I’d be crashing it because I’m not really a time traveler, though I suspect he wouldn’t be disappointed.
I’d try to satisfy my curiosity about things with similar laws of physics before checking out more different ones because I suspect it might be difficult to find your way back. There’s just so many variables that could change from universe up universe, and each one of those could be its own dimension you could travel along. It would be so easy to get lost, plus there’s a good chance I wouldn’t be capable of existing in an infinite number of them and would cease the moment I tried going to one of those.