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granted you want to hit Indianapolis, but like GLC said, maybe make Seattle your LAST stop and go from Florida to California, then up to Montana / Seattle and then head into Canada?
of course it all depends on how much you want to hit Indianapolis and if you have to be in Canada with family by a certain date. otherwise like i said above, i would start in Florida, maybe forget Indianapolis (at least for this trip), go West, hit California, and then go up to Seattle then Canada.
a lot of people seem to enjoy the drives in California up to Seattle, so you'd have some GREAT sites to see that will surely keep you busy (although i wouldn't know myself).
just a suggestion!
also, most car rentals around me you have to be 25, not 21. and believe me, i've searched all through the midwest and some southern states (NC) and they all state 25 years old. so if you find one at 21, then awesome! otherwise, sorry to maybe burst your bubble :(
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Actually most rental companies will rent to 21-25, but there is a daily "young driver" surcharge, usually about $25/day. You will also need a credit card with a fairly high limit, a debit card will NOT work.
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Reconsideration
After taking into account all of your advice, especially @glc, I am trying to re-plan my trip, looking at a more realistic first solo trip. I wrote the first post late after a hard days work and I realise how unrealistic it really was. I mean 36days, cross country as not only my first solo trip, but my first time in America was pretty stupid to even consider.
I am going to start planning a trip that will last roughly 30 days, but with only 3 to 8 hours driving between stops with the stops being 3 day, 5 day, 7 day and the rest just overnights, so it is easy going and keep it to the west coast.
I have a general plan in my head, but need to work some things out, I will let you know asap what I am considering.
Thanks for all your help and I look forward to receiving more :)