I've stayed at plenty of hostels and was well into my 30s. I'm just not that impressed with the HI chain of hostels. I've stayed at a few that were nice. But most are just kind of bland and if you are unlucky, you find yourself surrounded with groups of school aged kids, families with really young children, or budget travelers in their 50s and up. There are plenty of hostels that are springing up that are purpose built to be more "flashpacker" places to stay - better amenities, WiFi, modern and colorful common areas. They may cost a little bit more for a bed than some of the cheaper, older hostels, but I found this type of hostel is usually where you find more people in your own age bracket (mid 20s to late 30s with more disposable income and who are safely past the hard partying phase of their lives. You just want to avoid anything that's too loud and geared towards those who like to party (you can do this through reading online reviews very carefully at hostelworld.com, hostelz and even sites like Booking.com or TripAdvisor often have reviews.
I don't think you should avoid hostels, and I agree that if you can afford it, always go for a smaller dorm room of 4 beds or less - especially if you are a light sleeper. I've stayed in a handful of dorm rooms that were 6, 8, 12 and even one that was up to 20 beds only because it was all that was available. It's worth the extra money to have fewer bunk mates flipping on lights in the middle of the night or very early in the morning, coughing, snoring, etc. Besides the ability to easily be able to interact with other travelers, some of the perks of staying in a hostel would include access to staff to ask questions or get recommendations, use of the communal kitchen or laundry facilities, free continental breakfast (in some hostels - not all), budget meals (again, not all, but some hostels will have certain nights when they offer guests a hot meal for dinner at a relatively cheap rate).
But you should also look into other options for budget lodging. As mentioned in an earlier post, the Accor chain has hotels throughout Europe. Ibis, Ibis Styles, Mercure, etc. I've stayed at an Ibis during the summer for as low as 60 Euro per night while many hostels charge about 30-40 Euro for a bed in a shared dorm. The Ibis will have A/C and a far more comfortable bed. Just don't expect a whole lot of European "charm" in the decor - think "Hampton Inn" or "Comfort Inn".
In addition to hotels, look into university lodging (many colleges and universities offer up empty private dorm rooms to the public once school is done for the summer). You could also look at renting a private room in some local's home on Airbnb instead of renting the whole apartment. And if you really want to save your money for sightseeing or food, you could sign up now for a profile on Couchsurfing.com and see if anyone is willing to give you a free place to stay for the places you are traveling to. Doesn't mean you will have to sleep on a sofa in the middle of someone's living room - some hosts offer up private bedrooms with a real mattress. And as someone else mentioned, convent and monastery stays could also be an option - just expect the place to be pretty basic, clean and very quiet.