can i travel by private plane?

It's done in small towns across America every day.

It's how Kobe was killed.  He could have just as easily driven the 75 miles from Newport Coast to Calabasas.  It probably would have been less time early on a Sunday morning.

Sure. Here's the thing, you'll need a LOT more time to do so. Not only is your average private plane a lot slower than an airliner, but it can't (as in lacks the ability to) climb over many weather systems. That means you'll either have to wait it out on the ground, go around them or fly through them IFC. The latter 2 options are pants soilingly scary and you'll probably end up scud running to a predictable end. 

Yes, of course, it's why many people fly.  You don't even need to file a flight plan if the  weather is good (in bad weather you need to file an instrument flight plan).

@Steve P, the 120 knot plane in your example rents for between $100-150 per hour, not $350, and carries four people for that price... and you can fly to small towns that aren't served by airlines.

It's been done all the time since the end of WW2 everywhere.  Big farms and ranches.  Construction, oil and mining people flying from place to place.  Land on roads and cow pastures.  Doctors.  Nurses.  Dentists.  Lawyers. Taxi service.  Emergency medical.  Mail.  Even those who work in the City but live far out of the city.  Island to island Washington state.  Village to village Alaska.  Not an original thought.

I don't know what the Future Farmers of America has to do with flying, but of course you can. I know several people who fly a private plane as a means of transportation.

No.

Operating a car (with gas, insurance, maintenance, etc.) costs about 50 cents per mile.

Renting an airplane will cost about $350/hour.  If you cruise at 120 knots, that's over $2.50 per statute mile (five times as much as driving a car).  Plus, you'll need to rent a car on the destination end to get you to where you want to be.

If you are going somewhere 200 miles away, traveling by car would cost $100 and a little over three hours of your time.  Traveling by plane would cost about $600 and a little less than three hours of your time (time to get to airport, pre-flight the aircraft, file flight plan, check weather, fly to destination airport, secure aircraft, rent car, drive to ultimate destination).  So traveling by plane gets you no real time savings, but costs six times as much.

Unless you are travelling over 1,000 miles AND your time is worth several hundred dollars per hour, travel by private plane doesn't make sense.

 I live in the "back country" on the side of a mountain. Until a few years ago I flew an older Cessna 180 out to civilization quite often as my primary long distance transport.

 But maintenance costs and the fact that the airframe and instrumentation were getting 'tired' dictated that I sell it to someone who could afford the expense.

 I was considering purchasing another smaller airplane but the costs have risen to the point where it just isn't economically feasible any more.

I rather doubt that any such plane owner would be willing to just hand over their expensive property to someone they don't know, and I very much doubt that even if they were OK with doing that, that their insurance carrier would agree.