Generally the airlines run specials during the holidays and after the first of the year. Sign up for newsletters for your airline of choice and monitor prices. If you see an appealing price get it before it disappears.
I have found that booking the car a few months in advance gives you a better price. If you wait till a week or two before your trip the prices will go up.
I would respond to the "etc." part of the question. With regard to accommodation, when you have your itinerary basically figured out, go online and do a search to see if there are any festivals or special events in the areas you plan to visit at the time you plan to be there. If there are, you may either want to make your reservations well ahead of time to (hopefully) get the accommodation you desire or change your itinerary to avoid that area during the time of the event.
June would not be a generally difficult time during which to reserve or find accommodation; however, if there are certain properties or places that you really want to visit at particular times, you should make your reservations several months in advance.
I almost always recommend that people make the reservations for their first night (when they're tired and want to know where they're headed) and the last night (when you want to situate yourself close to the airport you'll fly out of). For June travel, you probably *could* get by not making reservations for the nights in between, if you're not terribly picky about where you stay. Most areas of the country, you will find someplace to stay.