Snow and sea in summer

If you want snow and sea in June/July/August, travel to the southern hemisphere where it is winter. Consider South America.

you are not going to see much snow in Europe during the summer ,as you are going to Zell am See you should be able to visit the Grossglockner Glacier and you may see some snow high up .

Despite the season, there is skiing year round on the glacier at Kaprun. So yes, there will be snow there.

Edit - Just quick look says it is doable, if a bit busy, but it is a long way from KL, so you can be forgiven. One thing that popped out was the June 11 Zell a S to Salzburg. You can take an REX train at 1:15 or 3:15 pm with an Einfach-Raus ticket for 34 EUR total (17pax). Train is direct, no changes in 1 hr 36 min. There are other little details like that which can be fine tuned. Czech trains are very cheap bought in country.
Also, Rick Steves suggests you try the "world's stinkiest cheese" in Olomouc.

Thank you so much for all your advice. May I know if i should consider kitzsteinhorn or grossglockner to see snowy mountains. I understand Austria transportation is very efficient so I assume my pack schedule should be ok? Any comments about my greece itinerary as I read that they are quite unreliable.
Appreciate much. And yes, we will certainly try the stinky cheese in olomouc. Thanks Rick.
PONG

Olomoucké tvarůžky is not that stinky, yes pungent but not bad , best way to have it is inside a potato pancake and it is on many pub menus throughout the Czech republic.

Any comments about my greece itinerary as I read that they are quite unreliable.

That's true for the trains but not for the buses (there is just one direct train to Kalambaka per day anyway). As a rule KTEL buses are reliable and clean. You would go by long distance bus from the bus terminal at Liossion street to Trikala and from there by local bus to Kalambaka. According to the Athens KTEL website (in Greek) buses leave

07.00 - 08.00 - 09.30 - 11.30 - 13.30 - 15.30 - 17.00 - 19.00 - 21.00

Book your seats calling 210 8311434 (or better: ask your receptionist to do that for you).

Still, your schedule is tight. The monasteries close by 4 or 5 pm, so in order to see the most important three (Megalo Meteoron, Varlaam and Hagios Stephanos) you would have to split your visit between jun 28 afternoon and jun 29 morning. You probably would not have time to escape the crowds and see the less visited Hagia Triada (access to which requires sturdy shoes). To save time, I'd stay in Kastraki on the road from Kalambaka to the Meteora (numerous hotels and restaurants of all types) and arrange with the hotel for a driver service in order to minimize walking times between the monasteries.

EDIT: I have just found out that the KTEL Trikala website has information in English:

http://www.ktel-trikala.gr/?module=default&pages_id=16&