Easiest weekend getaways are ferries to Batam or Bintan. No Causeway traffic jams.
It sounds like you are looking to chill out on the beach?
Very easy to stay at either Batam View or Turi Beach in Batam. Or if you want some town nightlife as well as the beach, stay in Nagoya (Batam's main town) at the Hotel Sahid Rashinta - nice garden villas in the middle of town. Excellent outdoor food centre right next door and 5 minutes from Nagoya's many pubs.
From Nagoya to the beach? Easy. Take the Batam View shuttle from in front of Lucy's Oarhouse. It will start running 18hrs/day from next week.
My favourite is to spend a weekend in the islands on a rough old sailing prahu. Sleep on the boat. Bikes and cooks on board. have a look at the Singapore Island Adventures website. Cant remember the URL - just do a websearch.
All these choices are very reasonably priced - cheaper than spending the weekend drinking in Singapore.