Booking.com is the the company that I predominantly use. You can start your search for hotels, hostels and campings right away from my website. Afterwards you find several other companies that I also use and you can use. They are all very different and you can decide yourself which one suits you the most.
Trivago is the largest hotel search site which scans more than 250 hotel booking sites worldwide.
If you feel like having your own private space, go for Airbnb. It is free and you will feel like you are part of the community.
Stay at the locals, join local events, meet up with locals, learn about their culture & get insider travel tips.