The Réseau Express Régional (RER) commuter express rail network (Line A) stops within walking distance of the park. Board the RER in Paris at Charles-de-Gaulle–Étoile, Châtelet–Les Halles, Nation or any other stop. Get off at Line A’s last stop, Marne-la-Vallée–Chessy, 45 minutes from central Paris. Make sure you take the right branch (Eurodisney is indicated on most signs). The round-trip fare is 12€. Trains run daily, every 10 to 20 minutes from 5:30am to midnight.
On Google Maps, RER stations appear as little white circles with the letters RER inside it. On French maps, line A is the red one.
So you could stay at any of the communities near an RER station. Take for example Noisy-le-Grand, which favours Eurodisney in terms of commute time and has nice accommodation offerings. Or Vincennes, which is closer to the centre of Paris and has more of a urban ambience. Or you could stay right in the heart of Paris at the Étoile. We can't recommend an accommodation by name and which locale you select along the RER line will ultimately be a matter of personal preference.
However, I do not think looking for self-catering cottages (of the sort you would find around Blackpool or Torquay) will be fruitful unless you look much further to the east, for example Château-Thierry, but the public transport connections to Eurodisney won't be good. You can also check the Paris - Airbnb site to see what accommodation is available from local hosts.
The RER is in the greater Paris transportation scheme and if you go between Paris and Eurodisney you would probably be most interested in the Paris Visite tickets. Marne-la-Vallée/Eurodisney is in zone 5.
The Paris Visite is an all-day ticket with four periods of validity:
one two, three or five consecutive days. It allows unlimited travel
within the chosen zones (1–3 or 1–5) on all modes of transport –
except the Jetbus network, the Filéo at Charles de Gaulle Airport,
tourist buses, and Air France services – and allows travel to Charles
de Gaulle and Orly airports.
Source: Public transport fares in the Île-de-France
See also: Frommer's France 2011