How to do Cinque Terre

If memory serves correctly, all except Corniglia are accessible by boat. All are accessible by train, but Corniglia is not directly on the train route -- a shuttle bus used to go from there to the town itself. Perhaps staying there, which is about midway between the towns on the "ends" of the string of five, would give you the chance to branch out in both directions. The RS guide book has a really good section on the CT that you might want to check out.

I have to say, I don't understand your statement

I have checked trains....all booked for these dates.

If you are taking a car, why did you book trains?

Setting that aside, you will need to get a reservation for lodging ASAP as June is close and lodging fills up. Everyone has a favorite town. Mine is Manarola, Ken's in Monterosso. At this point just get a place in one of the villages. Note that parking is difficult so 1) read Rick Steves' guide about the area and 2) ask at the lodging you secure for info on parking.

Once parked, you can take the train between the towns. It's just a few minutes between each. You can explore each town and maybe hike a trail out of each. You can take a train to one town and hike to another. Be aware there are many more trails than the over-popular #2, Sentiero Azzurro. Thie website is a nice guide. We like to take the little bus from Manarola to Volastra and hike to Cornelia, then take the train back.

It's not possible for trains around the CT region to be "booked up" as the majority are regionale trains. Schedules for those on Trenitalia are not available more than a week in advance but change very little so pick a day of the week - within the next seven days - and plug in a journey between any two of the villages to see a fairly accurate sample. As this is the off season, there may be more runs during high season. Tickets are only a couple of euros or so for each journey - depending on distance - so buy them when you get there. It's also possible to purchase a combo one or two-day trail/train pass for use of the trails and public transport but I don't recommend one of these if you're not planning to hike.

http://www.parconazionale5terre.it/Ecinque-terre-card.php

Trains are the most efficient way to get around and, as Laurel said, take only a few minutes from village to village: the entire distance from southernmost Riomaggiore to northernmost Monterosso is only 7 miles. And as she also said, driving/parking is a real pain so a lot of people leave their cars in La Spezia and take the train in from there (also a short/ inexpensive journey). Tickets MUST BE VALIDATED before getting on the trains, and the authorities are especially eagle-eyed here so be sure and do that as fines are expensive for having an invalid ticket.

You can take trains to all of the villages but Corniglia's station is at the bottom of the cliffs the village is perched upon. If you don't wish to make a strenuous climb, there's a green bus that runs between train station and village, and costs just a couple of euros if you don't have a pass. For fun, take the long stairway back down to the station as it's a lot easier than going UP!

Ferries run to all of the villages but Corniglia but are not the most efficient way to get around.
Expect both the trains and ferries to be VERY busy in June.

There are many trails in the park but the one you're probably thinking of - as it's the most popular - is the Sentiero Azzurro. It has 4 segments, and not all of them have been open over the past few years. I expect the section between Corniglia and Manarola to remain closed this year, the Via dell'Amore (between Manarola and Riomaggiore) may or may not be open; too early to tell.

You can check trail status at any time on the park's website:

http://www.parconazionale5terre.it/Esentieri-outdoor.php

The Sentiero Azzurro segments are 592-1 (SVA2) to 592-4 (SVA2) on the chart, and red-and-white circles mean that a segment is closed. This route is not "backpacker" difficulty but also not an easy stroll: expect lots of long, steep steps and grades to maneuver, and its going to be very busy.

Ditto Laura.

I have checked trains....all booked for these dates

Since access to the Cinque terra is almost exclusively by Regionale trains, and these trains never sell out, your statement seems to be mistaken. There are IC trains that serve Monterosso, but you cannot book them until 120 days out. You will have to wait another month to book trains for June. To look at the regionale schedule and prices, just pick a date in the next 7 days at www.trenitalia.com.

Regionale trains do not have seat reservations. If all the seats are taken, you stand, but you still get to ride the train.

Thanks to all for your help!

I have checked trains....all booked for these dates
The solution is simple: the present timetable on trenitalia.com runs to June 12th.

Where else are you going? 4 days is a lot in the CT. June will be mobbed & you might wish to move along after 2 full days, IMO.

I was there this September and the trains were very crowded. We paid about $24 for an all day boat pass and it was sure worth it. The lines to get on the trains were so long, I bet some of those in line had to wait for another train. We never had to wait for another boat. Weather does come into play with the boats however. We were only able to visit 3 of the 4 towns as the seas were too rough to visit one of the towns.

in October we took the train from the Pisa airport to Moneglia and used a B&B there as our home base. It is a couple of stations north of the CT villages. Granted this was the off season so you have to take that into account. I wanted to be out of the main a few miles and it worked out well. We went from out B&B to the train station at Moneglia each day for a trip we planned in advance. Some days we went to the CT villages and hiked to the next village and took the train back north to Moneglia. Some days were went north to other coastal cities and hiked and dined north of the five villages, always a return evening trip by train. We did Portofino, we went to Sestri Levante and hiked up the Punta Manara. The trains we handy, never over the top crowded. Those local trains cant be booked in advance so they are not full at this point. We also took two trips by boat, one back from Portofino to Rapallo then the train back to our B&B village. We also took the ferry from Monterosso to Portvenre one day and saw the whole CT from the sea. My point is there are numerous options for transportation, the trains, boats are easy to figure out so staying outside the 5 villages is an option. The only real draw back to this plan IMO is we did not have easy access for a quick trip back to our B&B in the afternoon for a nap or to rest...if you stay outside the villages your day is somewhat committed. We are in our 60's and a day or two with a short nap (wine tends to contribute to this) would have been nice. I had a total blast over there, hit me up on private for our B&B if your are interested.

Thanks again to all for the advice.