You have two issues to contend with.
Firstly, the power supply. A UK STE PSU is designed only to accept 220~240v so you either need to replace it with a USA 110v PSU or use a converter between your mains outlet and the machine.
Secondly, the colour video output will be PAL. You could run it into a standard VGA monitor, but you will be confined to hi res mono only. I don't know how easy/feasible it is to convert a PAL system to NTSC. You may be best trying to source a UK PAL analogue TV - you could get a PAL flat screen TV with a composite video in socket which runs on 12v DC. Something like this:http://www.allcam.biz/products/ptv.html
The power supply may well be auto switching (will work at 110-240v). If not, you should be able to source one easily through a local electronics store.
Out of interest, is there a reason for not using an NTSC STE? I wonder if it's a games compatibility issue or something?