What is your nightly budget for accommodation, in Euros? Mykonos has a huge choice of places to stay so without knowing what price you consider "affordable" it's difficult to make recommendations.
You have a choice of staying in Mykonos Town or at a beach area. Mykonos Town is not a giant party zone, so don't be worried about getting swept up in the party scene if you stay there. If you stay in Town, you can take a bus to get to a beach in the daytime. In the evening, you would be walking distance to scores of restaurants, shops and attractions (and bars/clubs, in case you decide you do want to go out one night).
If you stay at a beach, you'll be limited in restaurant choices and would have to take a bus into Town if you want a better selection or to see the shops. There would be fewer people around, though, and it would be much quieter (though lots of areas in & around Mykonos Town are peaceful, too.)
Either way, the bus rides are short (usually less than 15 minutes), so you basically have to decide if you would rather stay away from the hustle and bustle at a beach, or closer to all the action.
Platis Gialos and Ornos are two beach areas that have a good selection of restaurants along the beach, meaning you wouldn't have to go into Town for dinner every night unless you wanted to. Agios Ioannis is a nice beach area but has fewer restaurant choices. All three are just a short bus ride away from Town.
From Ornos and Platis Gialos, you can take shuttle boats to other beaches, including Paraga, Paradise, Super Paradise, Agrari and Elia.
Avoid staying at beach areas like Elia, Kalafatis and Kalo Livadi which are too far from Town and have very limited nighttime dining.