Croatia or Portugal in September 2015?

Try going to the Algarve area of Portugal--flying into Faro. The area's well serviced by budget European airlines flying out of London. The Algarve has a bunch of condos that are for rent and the weather will be perfect in September.

I can't comment about Portugal as I have never been there, but I was in Croatia in May. If you like hiking and destinations like the U.S. National parks, you'd love Plitvice Lakes. However, the park is about a 3 hour drive from Split, which is in turn about a 4 hour ferry/bus trip from Dubrovnik. If you want the great coast and beautiful water, I'd recommend Dubrovnik, the islands in that region, and venturing further south into Montenegro (Kotor, Budva). There's history and culture in Split, but not very much in terms of beaches. However, from that port you could easily head to Hvar, Korcula or one of the other islands. We went to Hvar and did a sailboat excursion that was pretty fun even though (maybe because of) the rough seas that day.

I've given you more than a week's worth of material for a laid-back trip. I would either do a trip centered on Plitvice Lakes and the islands or one centered on the Dubrovnik region including Montenegro. However, you may just go to Portugal instead. :-)