Montenegro is our easiest day trip from Cavtat — the border is about half an hour away — so we've ended up there over and over, both for quick day runs and for a longer loop around the country. The Bay of Kotor alone is worth the drive: it's a series of fjord-like inlets ringed with Venetian stone villages, and the road around the bay is one of the great coastal drives in Europe.
For the day-trip version, we'll leave early, drive up through Herceg Novi, do a stop in Perast and a boat over to Our Lady of the Rocks (the little artificial island with the church), then lunch in Kotor at Konoba Scala Santa, wander the old town and climb up to Kampana Tower, and finish with a coffee in Tivat at Porto Montenegro. Porto Montenegro is essentially a luxury marina built around superyachts — Kafeterija Porto is the spot. You're back in Cavtat by dinner.
The longer version we did was a five-day loop down the coast. We started with a scenic drive up to Lovćen National Park, climbed to the Njegoš Mausoleum (extraordinary panoramic views from the top), came down into historic Cetinje to see the royal museums, and stayed at Hotel Gradska. The next day we drove to Lake Skadar via the Rijeka Crnojevića horseshoe-bend viewpoint and did a private boat tour on the lake (monasteries, birds, very peaceful) before overnighting at Hotel Pelikan in Virpazar. From there we hit the Adriatic side — Ulcinj's old city walls, Ada Bojana for sandy beaches and fresh seafood at Restaurant Miško, the ancient olive tree at Old Bar, and the iconic island view of Sveti Stefan. We finished at the Regent Porto Montenegro in Tivat for the last night.
Montenegro is small enough that you can do a lot in a few days, and it's still meaningfully cheaper than Croatia. Kotor and Perast are the highlights if you only have one day. If you have more, Lovćen and Lake Skadar are where it gets quiet and weird and beautiful.