Your local city college may or may not offer free classes (in San Francisco, you just need to show proof that you live in the city with some legal status).
Some public transportation is free for certain groups (youth and folks experiencing homelessness can get free passes here).
"First X of the month" at the zoo/a museum/whatever
lots of venues have free events.
A jog, bike ride, hike
lots of great stuff outside!
If your baby isn't super fussy, the transportation difficulty (in our experience) is more in the logistics getting to/from airport, and dealing with other ground transportation. We just flew 5+hrs (coast to coast, US) with a 2mo and a ~3yo, and it was a piece of cake (typing that, I've jinxed the return flight...).
We haven't done international travel with our kids yet, but we will eventually. When I was 2 my family went to Europe
some countries were meh with respect to kids, but Italy (from my folks' retelling) was fantastic, as there is (or was) a big cultural love for young kids.
YMMV of course, but it's absolutely doable! Kids
even starting as babies
have personalities, and you'll get a sense of what's appropriate with yours. Good luck!