Ground fighting at darren de silva's place near clarke quay is highly recommended. Of course these days there are also many good places to learn ground fighting and BJJ styled grappling here. The judo place in lavender comes to mind. But having been at darren's for 3 years in the past, the atmosphere and people there are great and very willing to help. Highly recommended. He also teaches muay thai there. Privately, he can also teach you knife fighting, stick fighting, krav maga and etc.
If you wanna do stand up fighting, many good places here also. Contact Kinetics around Joo Chiat is good. Got a few friends who are the instructors there. Singapore has alot of good boxing places to train and also more and more muay thai places are coming up.
If you prefer to do a more traditional martial art....i suggest kyokushin karate or San Da