There are a lot of interesting answers, but I would like to maybe add a little more perspective from the "wife" point of view.
Maybe your wife is 100% convinced that hobbies should be put aside for parents of babies, and in that case maybe try to get the reasons why she might think so. But I guess everyone would agree that it is not a sustainable way to live in the long term, as it would lead anyone to loose themselves.
It is also possible that your wife can't see a way that she could have time for HER hobbies, so she feels that you shouldn't either. With our first child, I got resentful with my husband because I felt that he could just continue his life (almost) like before, while I was stuck with a baby all day and all hours of the night while on maternity leave. He would participate in some social events or accept engagements for work like it was no big deal, while I could not even come up with a way to go get a haircut. Is your wife breastfeeding? Your baby is still young, she needs to feed often and is probably not on a reliable schedule at this point, so just getting out of the house might be difficult or overwhelming for her. She might also feel guilty to leave the baby, for fear that she might need her when she is away, or that she will not take a bottle and will cry endlessly, etc.
I'm sure you appreciate all the hard work your wife do all day, but I just want to add that it is difficult for a dad to really get all the pressure that is put on a mother's shoulders. We as a society have LOTS of expectations about mothers and what they should do to be considered a "good" mother. Breastfeeding is also hard on its own, physically and mentally (the survival and development of your baby relies 100% on a bodily function over which you have little control, and this can feel crushing at times). And most of all, although you seem to be a good dad that share the chores and the work of raising the baby, make sure that you are not just "helping" her. Don't ask her what she needs or what to do, take initiatives. Read about babies and their development, be involved with doctor's appointments, plan for what your baby will need next (clothes, purées, etc.). Share the mental load!
So, to get back to your question... I will give you an example from my experience. With my first I almost never got anywhere without the baby for the first 6 months of his life. I was breastfeeding, but did not introduce bottles soon enough, so eventually he would not accept them at all. Why didn't I used bottles more? Because I would have to pump my milk, prepare a bottle, then make sure that all this stuff was washed and sterilized, etc. My husband actually giving the bottle was of little help as I had to do all the planning and he was clueless about it all. What I mean is, a mother can feel "trapped" even if she has a good partner. It is possible that your wife feels that you should sacrifice as much as she does in this parenting journey.
I think you can really help your wife by making her realize how good it actually feels to leave the house and spend some time doing things she enjoys on her own. She will need to experience it, and you will need to really help her organize it and make it work. There are many techniques to help a baby get on a routine, research them (I had success with the EASY method). Buy a breast pump and bottles so you can feed baby from time to time (and learn how to wash and sterilize properly). By the time babies are 3 or 4 months old, things get easier and more predictable. When your wife will have her own time for herself out of the house, I bet she will gladly accept that you should have yours too.