Alex,
It has been a while since I was in my 20s (it was the 80s and 90s). I traveled solo on multiple trips during that time and continue to travel independently. Some of the places I visited solo in my 20s included Greece, Germany, Austria, and Switzerland, Scandinavia, UK, and the Netherlands.
In my 20s, I stayed mostly in youth hostels or places that I found in Let's Go book. One of the nice thing about youth hostels is that you meet other travelers who are on a budget and so you often find people to eat meals with or go sightseeing. On a number of occasions, I met other young travellers and ended up travelling with them for a couple of days before we split up and went our separate ways. For example, I spent a couple of days in Germany with an Australian brother and sister. I shared a room in Flam, Norway with a young woman whom I met in the Oslo youth hostel after we arrived in Flam only to find the youth hostel fully booked. I had dinner with a woman from the UK in Copenhagen following a tour; two weeks later, I ran into her in Stockholm and we went to dinner again. In Baden-Baden, I went to the baths with the 3 girls I was sharing a room with at the hostel and we then travelled together the next 3 days. While it has been awhile, I am sure that there are still many young solo travellers.
I still frequently travel on my own and in general find Europe to be quite safe. I particularly enjoy taking walking tours in cities that I visit. Also, don't be afraid to go have a meal by yourself or get a class of wine at a cafe. It helps to be a little bit outgoing when you are travelling on your own. Ask fellow travellers for advice when you meet them. You will find that you meet wonderful people from all over the world.
