Well, you'll be travelling in high season. In both Venice, Florence and Paris you'd pay around 25-30 EUR for a hostel bed. So a rate of 17,20 EUR for 1-2 people with a small tent is actually quite cheap. And the shared tents in Venice and Florence are definitely the cheapest place to stay in these cities.
Budapest will be a good city to visit. Hostel beds in Budapest go for around 10 EUR per night. There is also a camping site (www.hallercamping.hu) in Budapest, but they charge you the same as for a hostel bed. (For Budapest I do not recommend pitching your tent anywhere close to the city outside a campsite, you might get robbed.) The better news though: Compared with the rest of Hungary Budapest has high prices. Hit the Balaton lake and soak in the thermal springs (Balatonfüred) or party the night away with Viennese students in Siofok. Along the Balaton you can expect to pay around 6 EUR per night for a spot on a basic camping site.
The Via Claudia Augusta has some nice scenery, but I do not recommend hiking on it. It is designed with cycle travel in mind, so parts of it are on modern roads that can be quite busy. Ok for a cyclist, but not ok for a pedestrian.
The problem with most old Roman roads in Europe is that they have never fallen into disuse - they weren't preserved simply because it was just a road. A road that needed to be fixed so that people could use it. Quite a few major roads in Europe date back to Roman times, so what happened to the Via Appia is nothing unusual. You can sometimes see stretches of old Roman roads that have been preserved because the route changed in modern times (because a bridge was built a little bit further down the river or lava from the Vesuv covered up the road), but this is the exception.
And since your Eurail pass is already paid for (I assume you still have the 2-months-unlimited pass?) you better use it as much as you can. That means travelling by train to each and every destination, not long-distance hike to it. Try to average around 2 hours each day by train or you would have been better off with point-to-point tickets.
Holland and Austria are not cheap, btw. You cannot camp wild in the Netherlands, you always have to pay for a camping site. And Holland is a country of bicyclists, you'll look quite strange hiking along the "fietspads"!
Only Wadlopen, a hike in the Waddensea would be something that could be worth a detour. But it needs to be done with a guide and you'll have to pay extra for this guide (10-20 EUR):
If you want some nice hikes I would recommend that you check out Saxon-Switzerland just south of Dresden. A cheaper area than Austria and enroute from Prague to Berlin.
Tip: Check out the "Malerweg". Most practical would be from Schöna at the Czech border to Königsstein a little bit further down the Elbe river. Just get off the train from Prague to Dresden at Schöna trainstation and you can start your hike. I've cycled down in the Elbe River Valley and views are pretty, even from below. Visit the Königstein Fortress at the end of your hike, then catch the train to Dresden from Königsstein train station. Or if you have some more time stay overnight at a camping site in the area - the Bastei at Rathen across the river from Königstein is a must.
Another good spot can be the Sumava National Park near Cesky Krumlov in Czech R.. You can take the train from Cesky Krumlov right into the National Park and from there you can either hike around the Czech side and go back to Cesky Krumlov or cross on foot over the old "Iron Curtain" (yep, parts of it are still visible) to Bavaria.
In Germany the most popular long-distance hike is the Rennsteig. It takes about 8-10 days to hike the full length, there are emergency huts everywhere where you can sleep for free (but be prepared for them to be full). This hike is in the Thuringian Forest sandwiched between Bavaria and Thuringia, it is Germany's version of the Appalachian Trail (on a much smaller scale though).
And I also recently stumbled about this article on wikipedia: http://en.wikipedia.org/wiki/Countrywide_Blue_Tour_in_Hungary
I openly admit though that I am more of a cycle-tourer, so I am not the best person to ask about hiking.
[ Edit: Edited on 19-May-2009, at 09:41 by t_maia ]