We stayed at the place next door to Diana last year (Odyssey).
We have 3 young girls (7, 3 1/2 and 1 1/2 at that time last year) and we had no problems walking everywhere/anywhere for dinner and did so every evening, apart from when we went to Fethiye via dolmus or water taxi.
There are restaurants like Guvens about 5-10 minutes away (really good food and very relaxed but attentive owners if that makes any sense) but the prom and all the other restaurants mentioned on here are no more than 20 minutes stroll away. Even with a push chair and one of the others on my shoulders... My timings might be slightly off but basically the walk involved to/from the start of the prom and then onwards to the far end is simply not a problem and doable even with small kids with little legs. The initial road is a bit rough past the bins
We used to occasionally get the dolmus back if we were out at the far end (by Meeting Point) and if it was getting a bit late but we also were happy to walk back from there too as we used to get a Slush Puppy from the bloke on the prom. Living the dream!
We are back again to Odyssey again in 3 weeks for 3 weeks and we really enjoyed the location and the walking never got too much or a pain...with teenagers that might be different though unless you confiscate their iphones etc to dangle as a carrot and to make them look where they are going