[Caballero]

Honestly, If you're only going to be there for a few weeks, it's probably not going to matter which variety you're exposed to. You'll still have your foreign accent which will frankly mask any regional accent you may pick up. What's more important is just to practice speaking and listening. Actually, although it is a marked accent, Andalusian Spanish is probably the most neutral accent to learn, as it is in between more northerly dialects and Latin American Spanish dialects, as they are all based mostly on early Andalucian Spanish.
A better criterion for picking a city to go to, is not whether they have a regional accent, but rather whether they are likely to switch to English when speaking to a foreigner, as some people have had the experience of going to a foreign country, only to find very few people with which to practice the language. And remember, there is no neutral variety of Spanish, the dialect spoken in north and central Spain really is just as marked as other varieties--more so in some cases. And remember, you can always recalibrate your accent if you spend a few hours when you get back home, to whichever accent you like best. What's most important is just speaking to native speakers as much as possible, whichever accent they may have. It won't corrupt you, don't worry. The most salient differences are the seseo/distinción/ceceo (pronouncing c, z, and s as "s"; pronouncing c and z as th; or pronouncing c, z, and s as th). You can use the spelling to help you out figure that out. Since you'll be there for such a short time, you won't really pick up on the intonation, so you should practice this on your own.