I understand what you meant but it would be an *economic* reward to have a U.S. military base in Poland. Why do you think the American cities fight like hell to keep theirs from closing?
Most Poles are aware that it will be kind of dangerous too. Big foreign millitary installations are always a risk to the host country for the following reasons:
1. If the host country is not consent with a planned millitary action of the guest who runs the base, a clash is preassigned. I.e. Turkey was against the recent Iraq war. Their refusal to let America use its millitary installations on Turkish soil troubled the realtionship between both countries, although they are NATO-allies. Politics change and politicians change. This is one reason why America wants to have its GIs out of Germany since they can not trust into the political situation anymore. If i.e. Merkel is loosing her job due to reasons we do not know in the moment and the combined left of Germany takes over power (PDS/SED/WASG/Linke, SPD, Greens) they would shut down the German airspace in such a situation like the recent Iraq war. The relationship between both nations would be heavily damaged in that case. The benefit that Germany has of US troops is much smaller than the damage out out such a (theoretical) political conflict. This is the reason why many Germans are not that unhappy that most of the US troops are leaving. You could say with some bitter sarcasm that Germany has more political freedom if they are gone.
2. US-installations are a invitation for terrorists/rogue-nations to start their actions in places that would have never been interesting to them. Poland or Romania i.e. are no natural targets of islamistic scum. That will change if 20.000 GIs are living in those countries.
3. The economic benefit for eastern European countries as a whole is rather low since those new bases do not have the massive manpower of the "cold-war-bases" in Germany anymore. They are just infrastructure to huge deployments in the case of a crisis. There will be some local effects and a few orders for the contruction industry, but nothing really impressive.
4. Poles and other eastern Europeans are proud people who want to take care of their security matters alone. We should understand that they have a long tradition of German occupation and Russian de-facto-occupation. Therefore they like their own uniforms best. That has nothing to do with anti-Americanism like in some parts of western Europe.
I do not want to provoke, but I hope to give some insight into the reason why some (in other respects very pro-american) eastern Europeans are against massive US-deployments.