Hi Mimpikami
Jimbaran have a lot of high end hotels and I never noticed anything in the mid-lower end. I would go a bit further south onto the Bukit and maybe try Balangan or Padang Padang areas - between Jimbaran & Uluwatu.
Balangan beach was my favourite in Bali until I fell down the steps there and it put me off going back in my last few months in Bali. There are several places to stay up overlooking the beach. I can't think of any names but a Google would bring them up. They all look nice. There are several warungs on the beach where you can get meals.
I have a whole album of Balangan photos on FB if you are on there add me and see if you like the look of it.