Transportation to Burg Eltz

If on the weekend, you can catch a bus at Hatzenport station which has connecting trains from Koblenz. Other times you can hike it from Moselkern. Its about an hour hike, sometimes a tad strenuous, and dry weather is a must.
http://burg-eltz.de/images/stories/doc/burgenbus_en.pdf
Stay north of Bacharach so you will be in the VRM transport district. That way the whole gang can ride trains and buses on a single VRM Mingroup ticket for 21.80 euro, or 3 days for 43.60.

A day trip from Bacharach to Burg Eltz is absolutely possible (I've made that trip), although it will be a bit of a long day. I assume you're planning to travel by train? As mentioned in the previous reply, there are several ways to reach the Castle, depending on which day of the week you'll be travelling. Have a look at the official Burg Eltz website for all the details.

A few thoughts on the travel methods......

• If you're energetic and want to hike from Moselkern, I believe that will take about an hour (of course not a good option if the weather is bad). As I recall, there are lots of signs near the station to provide directions to the trail. You'll arrive in the valley below the Castle, then cross a small bridge and walk up a stairway to get to the entrance.
• If you take the Bus or other transit, you'll be dropped at the car park above the Castle. From there you can either walk down the paved road (it's very steep!) or take the small Shuttle Van (about €2 PP each way). I'd suggest walking one direction and taking the Shuttle the opposite direction, as there's a great vantage point for photos about half way up the hill.
• One other Taxi service that's not mentioned is Taxi Ewald in Löf, but may not be the best option as they don't speak any English as I recall. Using a Taxi will be a more expensive option, so best to look at the other methods first.

About the only "castle" in Bacharach is Burg Stahleck, which is a Youth Hostel. It's above the town on a hill so has fantastic views of the river, and even if you're not staying there you can wander up there and have a "cool one" while admiring the views. There's a trail through the woods, which starts at the ruins of the old church. You could also have a look at the ruins of Burg Rheinfells in St. Goar if you have time.

My wife and I hiked down the trail to Burg Eltz, about two Kicks, but the hike up was trying as we had just landed the day before. Look into renting a car. They are cheap in Europe compared to the US and that will give you much more flexibility and time. An added plus is the car GPS system--in any language you want--it's a real travel boon to European cities and towns.

There are two castles in the Rhein-Mosel area that were never destroyed and have been preserved. Burg Eltz is one, on the Mosel. Just outside of Koblenz, on the Rhein, above Braubach, the Marksburg was taken over by the German Castle Assoc. hundreds of years ago and preserved as it was as a working castle. Cross the Rhein at St. Goar and take the train to Braubach. The walk up to the castle is not difficult and you won't have the expense of a rental car.

From St. Goar, a VRM Preisstufe 6 Minigruppen Tageskarte (21,80€) will cover the four of you from St. Goar or Oberwesel to Braubach and back.

See both Marksburg and Eltz if you'll be in the area a few days. You can see Marksburg more easily than Burg Eltz, and Marksburg is very good - if you only see Marksburg, I think you'll be impressed.

The scenery in St. Goar is outstanding, and I suggest, for this reason and for a good strategic location as well, that you stay in St. Goar, which is also the home of Rheinfels Castle; as pointed out above, St. Goar is in the VRM transit district, and you can take advantage of the mini-group ticket day pass. As Lee suggests, cross the Rhine from St. Goar (THIS FERRY runs all day long) and catch a train north to Braubach every hour or better, train ride is 22 minutes.) It's about 20 minutes uphill to the castle from town, or maybe you can catch the TOURIST SHUTTLE if you want. Note that the ferry crossing is covered by the VRM day pass too.

Marksburg Castle tours in English are at 1:00 and 4:00 in summer, or you can grab a pamphlet and join a German tour.

From St. Goar you can visit Bacharach (10 minutes by train,) Oberwesel (5 minutes) and Boppard (10 min.) You really don't need a car here.

If you make it over to Eltz, the train ride is about 1:10 - 1:20 each way. Then the walk is an hour or so hike each way. On weekends there's a bus from Moselkern (but only 4 per day) that might save you a little time, but the walk is pretty easy and very nice. My mid-70's in-laws had no trouble with it.

HIKE TO ELTZ INFORMATION

"We are a family of 4 with 2 teenagers."
You might want to inquire about the Rhineview unit at the Loreley Apartments - it was great for us.

Everyone has provided such thorough and useful information. Thanks to all, and we look forward to our time in the Bacharach-St. Goar area! Elizabeth