Diocletian's palace is very cool as it is
still a living city. So plan to not only walk around but to sit and have coffee and lunch etc in the city itself. There is at least one antique dealer with coins in the northern
part of the old city.
The Split Archaeological Museum is about a ten minute walk NW of the old city and is worth a visit. There is a fairly
cheap paperback 4-volume set of their numismatic
collection for sale at the gift store.
The ruins of the city of
Salona are located about a 15 minute drive inland from the palace
area. Not a huge lot to see but nice to walk around - they have an earth and
stone amphitheatre and other ruins and great views.
Cheap taxi ride.
Not
Roman but the small
medieval city of Trogir about half hour
north of Split is worth seeing. Also the drive from Split eastwards up the gorge to the high plateau is stunning though not doable if you don't have a
car.
Not much between Split and Dubrovnik. However it is worth considering building in a
side trip to Mostar in Bosnia & Herzegovina. It is about 45 minutes up the Neretva river from the coast. The
border crossing at Metkovic is usually a breeze to get through. You have to check beforehand though what if any visas you need. If you go this route you have to stop at the awesome little
medieval walled town of Pocitelj
part way to Mostar. Most people drive past and don't noticve as they never look up. Check it out online before you go and tour the castle and hike up the walls. If you really want to explore you can take a 20 minute detour from the route back from Mostar to Vrelo Buna at Blagaj where a 50' wide cold trout-filled river
comes out of a cave at the base of a 500' sheer cliff. There is a 500 year old
Ottoman Sufi "monastary" you can tour and several awesome
fish restaurants on the riverbank.
Dubrovnik is nice but is post-Roman. It is worth going 15 km south to Cavtat which was the Greek Epidaurus and the
Roman Epidaurum. It was sacked by the
Avars in the 7th century and the survivors fled to found what is now Dubrovnik. On a clear day you can
still see pillars submerged in the sea as you walk around the small peninsula. The best way to get to Cavtat from Dubrovnik is actually by small boat that catch at the Dubrovnik harbour. If you go that way you will pass my favourite little holiday spot in the
area - the tiny village of Mlini.
Hope that helps a
bit.
Shawn