As mentioned above, hotels around the Clarke Quay area would be ok. I would avoid all Hotel 81s, I haven't seen any good ones of them anywhere in Singapore to be honest! I did have a wee giggle when you said you didn't need to be around a shopping centre, very hard not to in Singapore, they have over 250 malls lol It really comes down to budget with your hotel choice too. Here's a link for trip advisor...
http://www.tripadvisor.com/Hotels-g294265-zfn18540-Singapore-Hotels.html
Busses and the train (MRT) are excellent, just buy an MRT Ezi Link card (like our smart rider cards) from the MRT station and you use it to tap on and off the train and buses, cheaper than you would by paying cash. Oh NO change will be given on buses by the way!!
A little tip if using taxis. Call the driver Uncle (male) or Aunty (female) while talking to them, they will think you are a 'Local Angmoh' and less likely to take you on a wee detour