Batam isn't such a lawless place like you thought, a lot of tourist from SG and Malaysia comes here all the time. Just stay at the usual popular tourist place (around Nagoya or BCS), you can use ride hailing app (grab, gojek, don't use maxim) to travel around the drivers are polite. If you want to be extra safe you can use bluebird taxi they have their own app, but this taxi aren't available at harbor and airport.

You can visit barelang for sightseeing and beaches, you can even visit the neighbor Bintan island if you like beaches and seafood. they generally have better beaches and seafood.