I feel just as safe, if not safer, walking around in Bali as I do in Perth. You'll find your hotel will be near lots of restaurants in easy walking distance. Lots of taxis are also available if needed.
You shouldn't have any troubles at all. Maybe take a torch as there can be holes in the ground. Be a little careful of your handbag but it's all just common sense and standard precautions. I often walk around with my children - nothing bad has ever happened.
If walking from the Samaya up to Eat Street, the only safety issue is the traffic as you'll have to walk on the road a while due to lack of footpaths. Probably a 10-12 min walk. There are a couple of casual eating places near the Samaya though.
I have been to Bali many times and during my holiday I always walk with my husband and or with friends. I would not normally walk the streets in my city at dark on my own so therefore I always carry that safety precaution anywhere I travel ... Bali is a safe place to be as long as you use common sense and always tell someone where you plan to go and stick to main roads you will be fine. Bali people are truly beautiful souls. You will find that most tourists walk late at night also as they are making their way out to dinner and bars. Hope you have a wonderful time.
Exercise standard precautions - like money in your wallet in a pocket - leave the handbag in your room - be aware of where you are and who is around you
Been going to Bali for many many years and never had a safety issue