Ved Niketan Ashram
This is one of the most known ashrams of Rishikesh, where you can still find a room for 150 rupees (single person room with common bathroom), although it might look like a real monk's cave. The price will include though daily yoga sessions in the ashram's spacious hall. There are also rooms for 250 rupees, 300 rupees, 400 rupees and 500 rupees, although the ashram is very often full.
Follow the Market road in Ram Jhula (just turn right after crossing Ram Jhula bridge) until the end.