Budapest, as far as Slovakia - Bratislava is on the border with Austria, so that's an easy answer for you (prices there have been rising in line with local demand and supply, so it depends on property type and exact location, good property in popular area is going up by around 10% p.a).
As far as areas close the the hungarian border, those close to Bratislava are fine, that is, near the three borders area (SK, Austria, Hungary). Now, in all southern Slovakia, the areas bordering on Hungary are the poorest in the country (along with the eastern Presov a Kosice regions). No growth there and no demand for property, young people mainly leave for other areas/cities, unemployment often 30%. Wouldn't touch a property there. Yes, its cheap, but for a good reason, there's never been demand and won't be later either.
Btw, I think it's foolish to expect prices to grow just because a country joins the EU. Yes, in the long term, but immediately?! In most places that joined (incl. Slovakia) prices actually dropped right after EU entry, and then got back to normal several months later. However, in Bulgaria the market has been so inflated by foreigners in last few years, it may take 10 years for the local market to afford the current prices (as you all know no locals are buying, all these many thousands of new flats in the sea & ski areas are sold to speculators with no resale chances... and it looks like very few rental chances).