The two main airports serving the Montenegro coast are Tivat (TIV) and Podgorica (TGD). Tivat is by far the most convenient for beach holidays — it sits right inside the Bay of Kotor and puts you within 30 minutes of Kotor, Budva, and the Lustica Peninsula.
Podgorica is the national capital's airport and is better if you're heading to the south (Bar, Sutomore, Ulcinj), though Tivat is still manageable from there with about a 90-minute drive.
A third practical option is Dubrovnik Airport (DBV) in Croatia, just across the border. Many travellers flying into Dubrovnik take a taxi or shuttle south to Herceg Novi or Kotor, which can take 45–90 minutes depending on border traffic. Check visa requirements if you'll be crossing from Croatia into Montenegro.