Just want to emphasize this. At this stage nothing is as great as me time. Well, I got a 6 year old and nothing is as great as me time still! When ours was smaller I made it a habit to take baby out on weekends for as long as possible, depends on what you got in your area.

We have a science museum/aquarium thing nearby so I just got a yearly ticket for that and seriously for a while went every single weekend with the kid to that place. It gave entertainment for 1-2 hours, we had food there, it was great! Then some playground or whatever on the way back and we'd be out 4+ hours. Just an example. It doesn't matter of your kid is too small to actually do stuff wherever you go, it is just as great to just show stuff to them. Animals are always great, unless you are firmly against the idea of zoos.

One last thing. Going for groceries or cleaning the house while the baby is out with you is not me time! It will be tempting for whoever is not with the baby to finally take care if stuff, which sometimes needs doing. But this won't relax you. Maybe do 50:50 if you're really behind on chores but don't forget to also take care of you, read a book, take a walk, go to a museum yourself, whatever. That counts for both of you! Just saying this before you go to your girlfriend saying, I am taking the baby outside for a while, you get to clean the house, thank me later! Don't do that!