Oooh I am jealous, we came back from Singapore and Bali in June. Absolutely love Bali and can't wait to go back (now we're living in Australia it'll be sooner rather than later!)
Singapore is fantastic, the Singapore flyer is worth doing, we were in a capsule on our own as it was so quiet, gives a good view of the Grand Prix circuit.
Bali; Ubud is worth a visit, nice place to walk around, some interesting little shops and you can go into the palace courtyard which has a rather fierce guard so comply with the signs! Definitely hire a driver; their knowledge is superb and will take you anywhere you want to go for as long as you want and it costs next to nothing. I can highly recommend http://sannybalitours.wordpress.com/ we used him and he was fantastic. Decent safe looking vehicle (some of them seem to be held together with sticky tape and a prayer!)
Volcano is a trek to get the really good views (not easy with a year old baby in a sling!) but so worth it. Monkey forest is superb as long as you don't mind running the risk of having a monkey on you! I did this solo as thought it might be a bit scary for my 3yo. The monkeys and their surroundings are fab.
Bali zoo is a nice day out; you need to go with open eyes though, the safari tour was good, as were the shows but they do have obviously drugged tigers etc out for tourist photos. Our guide couldn't figure out why we refused to have our pictures done as its not seen as cruel there; its just their way of making money from the tourists. If you can look past that then the zoo is surprisingly good; take a swimsuit as it has a nice swimming pool included in the entrance fee.
Pura Tanah Lot temple: best seen at sunset really as it looks wonderful with the sun fading behind it. Get there in daylight to see it in all its glory then stay for the sunset. Only worshippers are allowed into the temple itself but the outside provides the tourist photos. If you do want to see inside a temple go to Goa Gajah (the elephant cave), its a temple in a cave, not huge but rather atmospheric unless you're there with bus loads of tourists pushing for their photos, its near Ubud so could be combined with a trip there as its a shorter stop rather than all day. If you are wearing shorts (men and women) then you will be required to wear a sarong. Women are not permitted to enter the temple if you are menstruating and a ceremony would have to be performed to make the temple sacred once again if a menstruating woman should enter.
Make sure you get out and about to local restaurants, in Sanur there are some really lovely places along the beachfront. Meals are super cheap and the Balinese can't be more friendly. However by the time your holiday is over you will be sick to the back teeth of being offered 'transport', 'massage' or 'glass bottom boat'. You will also be encouraged by the locals to 'looky looky my shop'. Remember to haggle, haggle and haggle. The prices to start are high as haggling is expected. Take it as a bit of fun but remember that there's about 16500 rupiah to the pound and that whilst haggling is expected and fun not to take the mick as it is there income in a poor country.
Where are you staying in Bali? we always stay in Sanur at the Puri Santrian which has always been fantastic. We stayed at the Hyatt in Sanur once which was fine but the hotel is getting slightly dated. Still lovely though and nothing that amde the stay unpleasant. However we went to a wedding at the Padma hotel in Kuta which was stunning; the ceremony was performed in a a gazebo looking out to the sea and the reception was in the gardens of the presidential suite.
Have a wonderful time, we love Bali; its friendly, welcoming and great fun as well as being eye opening.