I don't have much interest in "going out" either.
Eating out: Often way too expensive. There's usually very little on the menu I'm likely to enjoy (I'm a picky eater), I don't trust the stuff they serve up to be entirely safe, and the background noise and overcrowding of many restaurants is too much for me. But there are exceptions.
Movies: It always seems much easier, and definitely cheaper, to just download a copy and watch it at home, but I used to enjoy going to movies back in the days when it was the only way to see them. There was always the risk of somebody with a big head sitting in front of me and blocking the view, or somebody with a big mouth chattering over the soundtrack. I'm somewhat attracted to "surround sound," but that can be done at home unless there are problems with annoying the neighbours.
Theatre: I do get something out of seeing a live play, but it tends to be rather expensive, arranging to be there can be cumbersome, they sometimes have awkward rules such as "if you leave the auditorium then you can't come back in until there's a suitable break in the performance". As with cinemas, there's often a risk of the person in front blocking the view or talking too much, though they seem to be a bit more strict about talking so that doesn't happen so often.
Live music: I used to enjoy it to some extent, though even when I really liked the band, I would get bored after half an hour or so. I think the shows used to be more affordable than they are now. Even with less well-known bands and musicians, I don't bother much at all, unless I myself can perform either with a band or alone. I like going to open-mic events and informal jam sessions. I've also quite enjoyed karaoke as long as I can use my own CDs for the backing so that I can rehearse and make sure the result is going to be fairly impressive. I'm more interested in what other performers do if I'm going to be able to perform too, because it gives me the chance to compare my stuff to that of others.
Seeing the sights: No big interest in that. I probably would if it wasn't so much trouble and so expensive just to look at a few things that seem over-rated. I've had some enjoyable vacations but they've mostly been in quiet places that aren't very commercialised.
I can't think of much else that people do when they "go out." It's important to me that I have some kind of a social life, but I prefer to confine it to visits to and from friends or performing music. Sometimes people I know will have a kind of music party where they feed everybody and have a jam session. I get something out of those, but while I'm not actually playing or singing, I feel like a fish out of water. I go along with it and hide my discomfort, but only because it gives me social brownie points. If the people are very much my type, it can be a bit different. Then I'll feel more relaxed and confident, and I might quite enjoy talking with them. I've even enjoyed the occasional party when the conditions have been really good.