Valentine is Walenty in Polish. The letter 'W' is pronounced as a 'V'. In any searches look for Walenty Markiewicz.
Do you have any more information about him? You don't give a birth date, but at that time Poland was partitioned and off the map, divided up between Prussia, Austria and Russia:
Immigration from Poland at the time your grandfather arrived would have been largely conducted at Ellis Island, New York, although Baltimore and Castle Garden were other destinations.
Looking at the Ellis Island website, there is a record of a Walenty Markiewicz arriving in 1903 from Bukomo. It is important to understand that information is not always 100% accurate. Names and places were often butchered when documented. I cannot find anywhere in Poland called Bukomo. However there are several places called Bukowo ( pronounced Bukovo ). It's possible he was from one of these places, but it's also possible that this Walenty Markiewicz isn't your relation. This is why it's important to get as much supplemental information as you can from family members or other sources.
If you register with the Ellis Island website you can look under 'action' on the right side of the record to view the passenger list, ship manifest etc
Here is the record I found:
Places named Bukowo:
Good luck with your search.
I have just checked and you will need to enter his name here:
For some reason his name doesn't appear after copying/pasting.