What is your budget? Everyones definition of cheap is different. Dublin isn't cheap in General from my experience. I went over 18 months ago for the night from Scotland, I stayed in this hotel
Trinity City Hotel Dublin | 4 Star Hotel Dublin City Centre which was really nice, clean and great service. I think its around 135EU per night which is about $150 USD per night right now.
Location is excellent, you could walk to Temple Bar area in less than 5 mins for food and drinks. It is also walking distance to cheaper areas of Dublin that won't charge you $20 USD for a drink. The local tourist attractions are well within walking distance if you wanted or you could pay 15 euros to get the bus tour of the city that stops at all the best tourist places.