I am not a Mykonos fan.. however.. our last visit we spent one day in Chora because it was the day we flew in and were beat.. but then we spent 3 nights on Paranga Beach.. and I DO recommend a stay there !!
We stayed at a hotel right across street from a gorgeous beach.. lined with little tavernas , and there was a nightclub on the hill that we visited and it was an amazing experience ( go for the sunset ritual.. its soft music being played while hundreds of us gathered on the slope overlooking the neighboring bay watching the sunset.. its was magical) We had dinner there too.. pricey but excellant food.. Scorpios , its a nightclub and a restaurant.
The hotel was not super fancy but had a lovely pool area, ( check out photos) and there was a public bus that stops right outside hotel that takes you to town in 10 minutes.. so you can visit the crowded chora but stay somewhere beautiful.
http://www.zephyrosmykonos.com/
We stayed at the Zephyros Hotel.. look at website.. its romantic and homey at same time.