I am arranging accommodations for my parents for a week or so in London and would appreciate advice on any neighborhoods and/or districts that I may want to avoid. They are in their early 70s and so I'd like to keep them out of any sketchy neighborhoods. Thanks in advance!
A lot of "good" London neighbourhoods can have some not so good streets.
If they are not staying in the West End, I suggest places around Sloane Square, Holland Park and South Kensington to name a few. Even Earls Court is quite safe and other places around West London are mostly fine (Gloucester Road, Fulham, Hammersith, etc).
SOme people might hate me for saying so, but I'd steer clear of Brixton, Hackney and Bethnal Green.
If you have any specific places in mind let me know and I'll give you my opinion. I know London well.
Plenty of reasonable hotel accommodation around, especially towards the west, as been suggested and around mainline stations. Just use common sense, especially walking late evening away from crowds where you might get the odd drunk or addict asking for money.
Central London's a lot safer than some like to paint it. 'Sketchy neighbourhoods' are far enough away not to be a problem.
If they're looking for (relatively) reasonably priced hotels centrally located, Bayswater/South Kensington tends to be the place. Absolutely steer clear of the row of cheap hotels along Finsbury Park which are awful, mostly DSS B&Bs really.
I agree with the others. West London is the best option for your parents to stay at. I live in east London which is proberly better for a younger crowd to stay at. If not, maybe try somewhere in central London could be an alternative, there are some decent and fairly cheap hotels you can snap up if you book in advance...
Like every city, there are good and bad bits in London. At the same time some people will enjoy areas that others didn't like at all and vice-versa.
The comment made about Hackney is acceptable, but I have had many good nights out in the area and in other parts of East London too.
If their budget is OK, then any London postcode with W, WC, SE and SW will do them good generally. Just be aware that London has crime right across it, from the penthouses to the bedsits. It's not unique in that though.