OP is young and just starting out on their own. Buying right away is likely not very realistic. Unless it involves staying with parents for several more years and saving up for the down payment. It doesn't sound like OP has yet done that saving, as they posed the question: do you think I need to save up before doing this, or something to that effect. Plus OP does not have a high income or a second income. Buying in JH might be a stretch at this point for OP.
We moved to JH as a money-saving measure 10 years ago, after owning a coop in Washington Heights for 23 years. So I can confirm: transportation to Manhattan/Brooklyn is much better from JH than from Washington Heights. We prefer this neighborhood in many other ways as well. The only way it falls short is that Travers Park is no match for gorgeous Ft. Tryon Park in Washington Heights.
Re: young people in JH, it's true that there does not seem to be a bar scene for 20s-30s here. I see young people renting in Astoria or Sunnyside and then eventually buying in JH when they have saved enough, have a higher income, maybe have a partner, have an inheritance...whatever. The housing stock for large apartments in JH is much better than in Astoria, Sunnyside, or even Forest Hills, from our buying experience. We couldn't find apartments anywhere near as nice in those areas as we found here.
As for price, we were looking at a particular price point 10 years ago, and we found we could get the size apartment we wanted at that price in JH, Riverdale in the Bronx, or Ditmas Park--or further out-- in Brooklyn. We decided we didn't like the Brooklyn options, so it came down to JH vs Riverdale. Maintenance fees were generally higher in Riverdale, and it is not well connected to Manhattan via public transportation in the area we liked, near the river. It has a very suburban feel, and you really need a car up there. It's pretty there with lots of natural beauty, Hudson River views, Wave Hill, outdoor swimming pool in the building we were considering.
But we chose livelier, better connected JH and are very happy with that decision. If OP can swing it, JH is a great choice, and maybe OP is not much for the bar or entertainment scene anyway. And the 7 train will get you to those other neighborhoods very easily.