Hi again,
From your choices the nicest place is Harrow but also a bit of a pain to get to Heathrow.
Hounslow and Hatton Cross are safe enough but not that desirable. If you continue along the Piccadilly line past Hounslow the areas improve until Chiswick and then start going downhill again.
Richmond, Twickenham and Kingston are ok too if you can get a bus across to Heathrow. Theres a very good site called Transport for London, the link for which is below. It'll give you a good idea how long and how many changes each journey will take.
http://www.tfl.gov.uk/tfl/
It sounds like you're on a budget so bear in mind the bus is now much cheaper than the tube.
Re my name, I'm from London but now live happily in the outskirts of Madrid. It came around from trying to explain my name to Spaniards who were interested in pronouncing it as the English do. Grey like the colour, then Ham but said with the London accent so the H is not pronounced. I then reversed the two words cos thats what happens in Spanish and ended up with Jamongris. Graham is very difficult for Spanish speakers, I had one person give up when I told her my name and just said I'll call you Pepe
It gets worse when I tell then my brother is called Brian......They sound very similar.