>>> Can anyone recommend a central Paris hotel, within walking distance to all the main attractions
Not unless someone can do an incredible shrinking act on Paris!
There are some European capitals (e.g. Copenhagen and Bratislava) where you can easily see most of the major attractions on foot. With some others (e.g. Berlin, Madrid and Paris) it's totally impractical.
So you need to accept that you'll need to use the RER and Metro trains , use the Batobus river service or take one of the (expensive) hop-on/hop-off tourist buses. Then you'll be able to look for a hotel anywhere within a wide area.
A useful hint for getting around is that, where possible, you should always use the RER train services, rather than the Metro ones. RER trains operate as a sort of 'limited stop' underground service, so they're far quicker than Metro services. They also tend to be less crowded. Many major attractions (e.g. the Eiffel Tower and Notre Dame Cathedral) have RER stations nearby. They also run to Versailles.
You can buy 'Paris Visite' tickets for unlimited travel on RER and Metro services (as well as buses and trams). Choose the 3-zone ones to cover most attractions, or 5-zone to include Versailles:
http://www.ratp.fr/en/ratp/r_61634/paris-visite/
The Batobus is a fantastic way to see many major attractions. It's a river boat service which runs from Notre Dame to the Eiffel Tower, with stops at major museums, etc:
http://www.batobus.com/en.html#
It operates on a hop-on/hop-off basis, so a 1-day ticket allows you see lots of places by paying just once for your travel.
Having got transport out of the way, I'll return to your accommodation needs. This website is excellent for finding cheap (but good) hotels:
http://www.hostelworld.com/
(I found a superb hotel in central Madrid three years ago through using that site. It had free wifi, excellent air-con and everything else I could wish for, as well as being spotlessly clean. It cost just €22 per night!)
Don't be put off by the word 'hostel' in that URL. Simply carry out an initial search with your dates and then, when you see a list of accommodation option, use the 'Filter' button, followed by 'Type' to select just 'Hotels' (and/or 'Bed and Breakfasts). Then read the reviews and, importantly, check the locations (to ensure that there's an RER or Metro service nearby into the city centre).
Looking at some random prices on that site (using sample dates in May), I'm seeing £47.56 per night for a double-bedded en suite room at the well-reviewed (and well-located) Luna-Park Hotel, with many others at around that price.