For Mainland, fly from Shenzhen. You can use ctrip.com to book the flight. Take the bus to Shenzhen (check the timings of the flights to make sure the Shenzhen Bay Port crossing is open).
From Shenzhen, good weekend options are Lijiang (very romantic!); Guilin (which you can also get to by train, which may be fun); Hangzhou (busy, but also scenic and romantic) ... and heaps of other places. Suggest don't fly more than 2 hours or you spend all your time in airports/on planes. China has air traffic issues, expect there to be delays.
Ctrip can also book hotels in China. Smaller hotels are very cheap and perfectly decent (not necessarily luxurious, but perfectly decent). I was staying in hotels in Lijiang, for example, for RMB 100-150 per night that were fine. Go explore You'll get far more bank for your buck in China, plus more experiences, than Singapore, which is bait "ho hum" and expensive accommodation. (drafted from a hotel room in Singapore!)