If you can get your average room rate down to $75 (ha!), then note that your average daily rental car rate will exceed your average daily room rate.

This is in the summer.

Alaska can be done cheaply (well, relative to the summer) in the shoulder or off-season--you can find much better deals on rooms and rental cars when you're not competing with 1.2 million other tourists. (Shoulder season would be May or September; off-season would basically be October through April. No one wants to visit Alaska when it's 5 degrees and there's three feet of snow on the ground.) In the summer, demand outstrips supply and consequently the prices go through the roof. Even the Anchorage Motel 6 starts at $139 per night in the summer.

That trip to Juneau will cost you a pretty penny any time of year, too. You can start in Fairbanks and work your way down to Anchorage (and make a side-trip to the Kenai Peninsula south of Anchorage) fairly easily, but to get to Juneau, you'll either need to put your car on a ferry or fly (there are no roads to the state capital)--neither of which are cheap: a $250 round trip airfare from ANC to JNU is a good deal. (You might be able to do it a bit cheaper as a stopover on an ANC-SEA flight.)

You can cut the cost down a bit--Priceline your rental car and stay in hostels in the larger cities and rustic cabins in between--but I'd still say that it's not feasible to expect budget travel in the summer in Alaska...

For more specific itinerary advice, try this search link and look at at least the first page of threads and perhaps a few on the second. There's been a lot of great discussion and advice in the last year or two about what to see or do. Perhaps you'll find some ideas there.