I used to work in Harrow and while there are extremely nice parts such as up on the Hill where the School is the town centre is a bit grimy. It has a reasonable amount of amenities, however. There's a reasonably good pub we tend to go to in the centre called the Fat Controller as it was just around the corner from work.
If you want to be close to transport links Harrow & Wealdstone is a bit of an option and is more suburban as it's heading out towards Bushey, Watford way but is still on the Bakerloo & mainline train service.
Harrow-on-the-Hill station is in the town centre and is on the Met Line and the Chiltern Railways line between Marylebone and Aylesbury. I don't know as much about South Harrow but having driven through there a number of times it's a bit urban grimy and doesn't seem to have the nice green areas.
If you head out Pinner/Northwood ways it gets very nice and more pricy and more green as well. But it's quite suburban in feel.
I have to say, budget-wise I wasn't greatly surprised by anything, ie things costing lots more. There are a few things here and there, of course. My biggest surprise was the price of a can of 4 tennis balls - minimum £4 in bulk - I can't believe they charge that much as you can get the same in the US for $3-3.50. Otherwise, I came from the DC area before moving over here where rent/housing was quite expensive anyway. Grocery shopping doesn't seem that much different in price and some of the food here is much better, more organic, free range. Train journeys are fairly on par. I suppose petrol is a lot more but I drive less (except when I expense it to my company/clients!)