Most major hotels provide hairstylists offering a full range of services. Hair salons are also found in shopping centres, offering standard haircuts as well as more elaborate services like hair perms, facial treatment, manicure and pedicure services.
Orchard Road is the major shopping area in Singapore. You will be able to find luxury goods like Chanel, Hermes etc and mass retail outlets like Marks & Spencer, Zara, Mango amongst other brands here. There are also two major bookshops- Kinokuniya and Borders. Kinokuniya is located at Takashimaya while Borders is located at Wheelock place. For cheap fuss free meals try dining at one of the foodcourts located at Takashimaya basement, Scotts Shopping Centre basement, Wisma Atria topmost floor etc. A full meal only costs about 3-5 SGD.
Far East Plaza is an enclave of youth fashion, it is also the shopping centre with the highest concentration of hair salons in Singapore. Pay it a visit for cheap fashionable clothing and shoes.
Lucky Plaza is where the Filipino community hang out in Singapore, thanks to them you can sample Filipino cuisine here and also buy goods from the Phillippines, there are also some electronics stores located at Lucky Plaza(however it is probably not advisable for you to buy those goods here) and 2 scuba diving stores.
The recent revamp of Marina Square shopping centre has injected new blood into the City Hall shopping belt, the 3 main malls here are Raffles City, Suntec City and of course Marina Square, the Esplanade is located a stone's throw away.
Those looking to buy electronics in Singapore can go to Sim Lim Square, Funan IT Mall (mostly computing stuff). Do note that some retailers at Sim Lim are blacklisted by the Singapore Tourism Board, you should look for the Star Retailers, they will have the sticker or icon displayed usually at the front of their store. Electronic chain stores include Harvey Norman, Best Denki. Mustafa Centre located in Little India is the only 24 hour shopping centre in Singapore, they sell everything from cabbages to ipods.
feel free to contact me for more information on any of the above.