Airfare SFO to Tallinn

That is crazy high for economy. A quick google flights search shows lots of options in the $800-$900 range. Is that a business class quote?

Google "SFO to TLL flights" and plug in your dates into Google Flights. You can easily find tickets < $1,000. I would not use a travel agency if they are quoting you something in that (outrageous) range. It's easy enough to buy your own tickets, it works just like domestic flights.

You can also try flying to a city like Amsterdam and taking an airBaltic flight directly to Tallinn, which may work out depending on the schedules that day. Just be conscious of the layover time, checked bags, etc. Ideally you'd want a few extra hours in Amsterdam (or wherever) to make that work. But having a long layover with two separate tickets could save you a lot of money.

Hop on Google Flights and see what your options are.

Ditch the travel agency and book the tickets by yourself. It's easy to do online, airlines flying to both Tallinn and San Fransisco are SAS, Lufthansa and Norwegian. And with codeshare you probably have more options as well. There is also the option of self connecting, but there is always a risk in doing that. Did a dummy search at SAS and they had fares for slightly less than €800. I'm sure about the current exchange rate, but I think that is a bit lower than $4000. Quite a long layover one way though, but on the other hand enough time to see parts of Copenhagen.

I would find another city of interest with dicount airline connection. For instance Berlin, London, Kyiv all under $100.

I’ve flown from SFO to Tallinn twice now on United; first was round trip in early September at approx $1000 and then just this year in late April open jaw into Tallinn and home from Budapest for $900. Both times with a couple hours layover in Frankfurt: definitely book your own tickets.

$4000 per person sounds more like a business class ticket than a coach ticket.