Before we begin, there are many different types of real estate investment, and many different parameters to look at. For this list I am focusing on investments that can be used as rental properties, while hopefully retaining the initial fiat amount plus appreciation

5: Italy
Italy is attractive for a variety of reasons but the fact that it is one of the most tourist heavy countries in Europe is the main draw. For a vacation rental, a place that gives good value should be close to the main roads as it could be a stopping point for tourists on their drives down the country. A sea view is great if you are thinking Amalfi, but price per square meter will be higher. Good values can be found viewing the countryside since viewing rolling hills of vines is perfectly idyllic. Property appreciation is not great unless you buy in a big city, but the investment amount needs to be much greater for that to be attainable.

#4: Malta
For those who don't mind buying island property, Malta is an excellent option. Popular with tourists all over Europe, tourism from America is increasing. The best place to look is probably Valleta. It is an historic city with great buildings and culture and property values are likely to retain their value. Also depending on how involved you want to be, AirBnB is a much more profitable way to make returns in Malta compared to traditional agencies. The main drawback is the fact that as a foreigner there is a minimum investment amount of around $100,000 for an apartment anywhere in the country.

#3: Croatia
Croatia is a magical country, and if some pictures look familiar you've probably seen them as the scene of King's Landing in Game Of Thrones. Once part of a divided nation, Croatia is undergoing a current Renaissance with tourism and art. In fact, they hold one of the world's largest raves (popular with young folks I hear).Property values for something worthwhile will range between $1,000-$1500 per square meter.

#2: Czech Republic
Surprising to many, a lot of people from America who travel Europe say Prague is their favorite city. What does this mean for an investor? Well, nothing now, but if we predict tourism rates to continue to increase Prague values will rise as well. You'll want to look in the old town even though it is more expensive, because that will net the highest tourist dollars. Other than that, the cost of living is fairly cheap so to hold it purely as an appreciative asset is not entirely dumb if you are just looking for a vacation home for you.

#1: Montenegro
Montenegro seems to fly under the radar of many real estate investors. It is similar to Number 3 on our list, Croatia, but has not yet seen the tourism numbers. That being said, price per square meter is slightly higher in the $1,500-$2,000 range. For a country like this you'll want a sea view. The main city of Budva is popular but really any little Villa or apartment around the Kotor Bay will be popular with long term European retirees looking to spend a month or longer in a more southern Europe atmosphere. While tourism is not yet high, the yields one will get from the tourists is, and that is why it is number 1 on this list. I see a good appreciation from asset value as well as rental yields and if you're in the market this may be a place you want to pay attention to.
Note: The views expressed in this article are solely my opinions and should not be taken as advisement. Rather, more as a starting point for where you can start your own research.