Bubbalor, I've been researching cheap accommodation in Paris (only wishful thinking unfortunately) and if you're going to stay at least a week there you might want to look into apartment rentals. We checked out family hostels first (there are 4 of us) but found several apartments that were much cheaper and looked great on
http://www.waytostay.com/ And with an apartment your food costs are a lot less as you have a kitchen.
I've stayed three times in Paris in the last three years using
http://www.myapartmentparis.com and been very happy each time. Just be aware that you must pick up your keys yourself from their office in the 10th district after 5:00pm so it's handy to be relatively close to there or figure out how you are going to get to your apartment. I like the 10th as it is not touristy at all but still has great markets and local shops for food etc. It is a little more of a recent immigrant area so can be a little bit of a culture shock for some (my 13 year old son had certainly never seen a street which was just African hair and beauty salons). Google maps street view can give you an idea what is around the location you are looking at.
Each time we stayed we used the Velib bikes to get around Paris almost exclusively. It's a great way to discover Paris - but maybe not for everyone. I had downloaded off line maps to my iPhone so knew roughly where we were going and where the nearest Velib stop was (you have to change over every 1/2 hour if you don't want to pay extra).
We did do the Fat Tire Bike Tours of Paris and I can recommend the day time ride as a great way to get a feel of what is around in a safe environment. The night time ride is also fun but is a little more daunting.
If you are thinking of extending your stay to do a bit of rail travel in Europe I would suggest using
http://www.seat61.com to plan your trip and figure out how to buy tickets. Do not purchase from Australian resellers unless you are super cautious - they charge an arm and a leg for what you can easily buy yourself online.
PM me if you want more details.