Europe is a notoriously pricey destination, where swank accommodations, lavish foods, rich history, and a consistently tough euro against the dollar all tally up to a hefty bill for any traveler.

But budget travel site Price of Travel has taken a closer look at European options within a certain means, with their third annual European Backpacker index that measures a budget for various cities in Europe. They have ranked a host of cities on the continent, and uncovered some surprising results.

Due to a European recession, they say, many countries have become significantly cheaper, especially those in the East. Now is the best time, if ever, to go. Here are just some of Europe's inexpensive cities, with attractions that satisfy both frugal and lavish travelers alike.

Bucharest, Romania

First on the European Backpacker index, Bucharest bears the low cost per day of 78.57 Romanian leu, (about 24 dollars). The capital city has been nicknamed "Little Paris," and is famous for its historical significance: enjoy the Romanian Athenaeum, a concert hall in the middle of the city. The interior's domed structure, decorated with rounds of gold and baroque design, is a once-in-a-lifetime sight to see.

Riga, Latvia

You can do Riga for only 14.60 Latvian lats, Price of Travel says. That's about 26 dollars a day to visit the capital of Latvia, a Baltic country nestled between Estonia and Lithuania. The city houses a number of trendy new bars and restaurants, as well as a centuries-old city center that can be explored on foot or by train. The skyline isn't too bad either: the Riga Radio and TV Tower greatly resembles the Eiffel, and the Baltic Sea just beyond eye shot lends a certain crispness to the air.

Zagreb, Croatia

Often, travelers opt for Croatia's more well-known beach and resort towns. But Zagreb is a stunning marriage of Eastern European classic antiquity and Western European modernity. For just 222 kuna, (about 38 dollars), roam this capital city for its numerous outdoor markets, 19th-century palaces and medieval architecture.