Looking for more places to visit ....

What time of the year and how many days (nights) in Greece, Budapest and Istanbul?
If it is only the mentioned 25 days then I would stay all the time in Italy. But as far as I see you need all your time for the mentioned destinations and really won't have time for adding Italy. Your trip is very rushed anyway.

I'm a bit mystified. You're traveling for 25 days. So far you are visiting 4 countries: Hungary, Turkey, Greece and Italy.

Are you not interested in exploring more in each country than the 4 cities mentioned? There is so much more to see.

Are you asking advice for other countries to add to the itinerary? With 25 days you could easily just immerse yourself in one country. For perspective, I've been to England 3 times in the past 8 years for a total of 42 days, and I haven't made it north of London yet.

Is be curious to see your itinerary so far in more detail so we can help with suggestions.

@jeanm ..... yes!!! I will love that! suggestions??? I'm so open to any suggestions !!
@allan not itinerary yet...just starting planing
we are just looking for pretty/interesting places to discover and enjoy...

I found Sofia interesting some years ago. Interesting and manifold history and still comparable cheap destination in Europe.

I travel in July too.

RE: "...we are looking for something different "

If you are entertaining the idea of different regions in a different country, how about North Germany and eastern Germany, ie towns and cities east of the Elbe River, lots of interesting and unique towns and cities in this part of Germany as to history, culture and geography.

I would definitely encourage you to stay longer in the identified cities/countries. Four days doesn't seem like enough time for Istanbul. Certainly not for the rest of Turkey.
Also, take a look at how you will get to Budapest from home (wherever that is). You could add a couple of days in the city you're flying into before moving on to Budapest. According to a quick search, there are direct trains to Budapest from Munich, which has a lot of direct transatlantic flights. Likewise, you can travel from Budapest to Istanbul via Bucharest (involves overnight trains, which not everyone loves), so that's an easy destination to add. You've already thought about this--i.e., stopping in Rome on the way to (or home from?) Greece, but maybe there is another option you haven't considered. Like a ferry from Marmaris via Rhodes.
These distances are pretty long by European standards, so you might prefer to fly between them.

About 2.5 hours south of Budapest by train is Pecs, a town filled with great cultural sites, good restaurants and alive-with-life people. The highlight is the town square and Kiraly Utca, which is known as the walking street. There are no cars, no noise, no fumes, no worries. Some of the buildings in Pecs -- the Town Hall, the National Theater, the Hotel Palatinus -- look like they were designed for a charm bracelet. Pecs was named a European Capital of Culture in 2010.

Pecs is packed with museums and religious sites. For me, the highlights were the Zsolnay Porcelain Museum and the synagogue. I had never heard of Zsolany porcelain, but the family-owned company was the biggest in Hungary on the eve of World War I. And the company's porcelain, especially the architectural systems, was stunning. The synagogue, which dates to the mid-1800s, was well described and once housed a thriving community, which was devastated by the Holocaust. I also visited the Csontvary Museum (art works by a beloved Hungarian painter), the Modern Hungarian Art Museum, the Cella Septichora (Roman crypts) and imposing cathedral. There even more museums for the real culture vultures.

Another great town is Eger, two hours northeast of Budapest by train. It's a charming town for browsing the produce market. The town hosts a great thermal spa. The Lyceum, a teaching training college from the 18th century, houses a glorious Baroque library -- 60,000 books in over 30 languages under a frescoed ceiling. The "Magic Tower" has a working 18th-century camera obscura.

In Turkey, I'd recommend Cappadocia, Antalya and Kudashi, a port town that will make you fall in love with the country. Kudashi is near Ephesus, the Ancient Greek city mentioned in the Bible. The antiquities are amazing. Other great antiquities are seen in Heliopolis, Aphrodisias and Aspendos.

In Turkey, I'd recommend Cappadocia, Antalya and Kudashi, a port town that will make you fall in love with the country. Kudashi is near Ephesus, the Ancient Greek city mentioned in the Bible. The antiquities are amazing. Other great antiquities are seen in Heliopolis, Aphrodisias and Aspendos.

I agree. Turkey is an amazing country and has so much to offer. It would be a shame to only spend time in Istanbul when there is so much more for you to see and love. I loved Cappadocia, and after that I went to Ephesus and Fethi Kama, which were just incredibly wonderful. Cappadocia has so much history and really interesting scenery. Ephesus is a beautiful coastal town on the Turkish Riviera, and Ephesus is the ancient Greek city where the apostle Paul spoke to the masses. You could easily spend weeks here, but even if you only spent an additional seven-plus days, it would be worth it.

waw!!! great ideas so far..thank you so much I will do some research of all those places!!! keep it coming please!!! thank you
(2 years ego when we traveled to Italy also for 30 days people in this site gave me the best advice, so many good places that I have never hear off and I added it to in between the major cities...so grateful for that!! ... so they become part of my Italian trip memories!

Thank you all

For reference Im traveling from Argentina.

While in Greece visit Delphi, Corinth and the Corinth Canal. Also, in Athens, do the New Acropolis Museum as well as the Museum of Archeology.