Well definately a romantic dinner on Kuta beach is a must do for a new couple.
My wife and i are super adventurous, so we did a whole lot of walking, even did a bicycle ride through a village and went up to the dormant volcano. But when we didnt walk, we made use of the same cab driver through out our stay. He was recommended to us by a staff member at the hotel who just happened to be south african. So we were guaranteed the best rates whenever we used him.
Id advise you to speak the the staff at your hotel for recommendations on cab drivers. It will always be the safer option.
Bali is mainly bhuddist. But Indonesia as a country is a largely muslim country. Try as much as possible to avoid going places with people you dont know.
A couple of locals tried to con us once with some scratch tickets, claiming we had won a couple hundred dollors. The catch was that we had to give them our hotel address so they could pick us up that evening and take us to where we could claim our prize.
Of course at this stage, instinct kicked in and i suddenly had images of wearing an orange overall and ending up on an ISIS propoganda video.
All in all, we had an incident free stay. Had loads of fun, and didnt break the bank to be there.
As with every new place, just be conscious of your surroundings,, dont take tours with non accredited tour companies and you should be good!