I think it's about a seven hour train ride to Berlin and most bases are a train change or two and several more hours away yet. Reading between the lines on the announcement it looks like this will be a foreign posting for several battalions on an accompanied basis. My guess is that the average Haus-spouse from Bavaria and Westphalia won't be too happy leaving their families and friends behind. for a multi-year posting.
It's not quite as simple as going for a one-time bachelor party for several thousands of young soldiers away from their homes and families for many months on end.
On top of that they'll have to build a brigade-sized garrison and sustain it indefinitely. That increases their base infrastructure by about 10% with an extra-national supply line. Lithuania is supposed to fund the bill for that but they are already signals from Vilnius saying it will be problematic. Lithuania has only four brigades (one a reserve one) and their pay and accommodation standards are much lower than what the bureaucratic and standards-happy Germans will demand. (They're not Brits for whom mouldy barracks are au rigueur. There are some estimates this will cost Germany some € 5 billion. It's easy to see why the German army is signalling concerns with the plan.