7 to 11 cassette upgrade or new bike
A 11 speed cassette would mean a new hub (probably a new wheel realistically) and likely a new derailleur to match the cable pull of the STI shifters plus the labor (this includes installation of the new cable stops, new cables, re-wrapping the bar after putting on the new brifters, etc.). You will also need to spread the frame to get a modern hub in there, which we can count under labor. 

If you want to keep the bike: You're better off putting on a new 7 speed cassette or freewheel depending on what you have (I'd guess its actually a hub that takes a freewheel) and either living with the current shifters (downtube shifters are lovely and incredibly reliable when you get used to them), going bar-end shifters, going Retroshift or putting a Shimano derailleur and using the 7 speed Shimano Tourney ST-A070 (there is a double &amp; triple version) or compatible Microshift shifters (SB-R472 for doubles/SB-473 for triples). 

If you want to get a new bike: The price of STI shifters and the fact that 7 or 8 speeds is more than enough makes a new bike (or a used bike with STI shifters) a good option unless you're particularly attached to this frame (and everything else is in decent condition or good enough condition that you're willing to bring it to acceptable for you).