Hi Fio,
Yes there are a lot of very nice resorts in Mui Ne.
I chose Bamboo Village because all reviews I could find were positive. The Beachfront Deluxe Bungalow was 135 USD but this is their most expensive room option (apart from family accomm) . There are other room categories for a lot less (starting from around 60USD depending on season, who you book with)
I booked through vietnamstaydotcom (found their website when doing a search for Mui Ne hotels) There's lots of good info on their site including area info, hotel info and current prices and a location map so you can get an idea of where each hotel is in relation to another.

Sea Lion was 75USD for seaview deluxe - good deal as it was a low price for such a nice room. Bungalows were 100USD - quaint and nicely done, but didn't have views of anything much and actually weren't as large as the rooms in the buildings. This resort was booked with vietnam-travelservices.com.

A lot of sites have Mui Ne listed under Phan Thiet so you need to check those listings as well as Mui Ne.