We stayed in Montemartre for a week in 2010 and it was wonderful. Easy access to train, buses and an easy walk up to Sacre-Coeur and the fascinating Church of St. Pierre.
Our daughter-in-law booked a small apartment on-line and it was quite cheap compared to staying closer to the city centre. Lots of accommodation sites to choose from - the apartment we had is now rented out on a permanent basis. Always read some of the reviews though, a friend didn't have as much luck as we did!
We took the second option from the above website and ventured a bit further to a very interesting old cemetery in an old quarry, http://www.pariscemeteries.com/pages/montmartre.html
Don't get caught with the sketch artists - they charge a lot! Some of them are very pushy!!!
Be prepared to walk a lot and it is quite steep in places but sooo fascinating. I hadn't had my hip done then but used my walking stick and managed quite well. Fell into bed exhausted each evening though!
We chose to eat in small and interesting restaurants - the Onion soup is mouth watering! Check out the small local bakeries too! The people are friendly and very helpful.
We did all the usual sightseeing in Paris - Notre Dame Cathedral, Eiffel Tower, the Louvre, the Rodin museum (my favourite), etc, etc. Took the hop on/hop off bus and walked many kilometres too. Again, we chose to eat in interesting smaller places - Middle Eastern, French, Japanese. All fabulous and not too expensive. Don't forget to try the wine too!