I recommend condo function rooms - if you stay in a condo! Otherwise, you can also book a place at Trehaus (co-working space) and it’s really lovely!!
We did ours at KidsAmaze at Toa Payoh. They have an infant play room. You just have to get your own caterers to come in with food.
Swensens has a good party package with games Master / host and all.
Bove at Suntec City