I'm planning on going to the Adriatic coast from Toronto next summer. I'd like to land in either Dubrovnik (DBV),Croatia or Tivat (TIV), Montenegro. I also want to visit London and Paris as stopovers for 3-4 days each. I know this can be done craftily with minimal miles but i don't know how. I have United, Delta, and BA miles to spend (economy seating). Can anyone shed some light on the best way to do this for the least amount of miles.

Thanks in advance.

It really depends on the amount of miles you have in each of those accounts as well as the dates and award space available. In this instance I would contact an award booking service like Juicymiles or Pointspros who will be able to give you advice on how to book and assist you with the booking.

UA permits one stopover on RT award travel. You might be able to get a stopover (in either direction) in London or Paris, visit both cities during that period, and then resume your journey. Look for connecting flights on LH, LX or OS.

Dubrovnik and TIV are tiny airports and do not have a lot of flights on alliance airlines, so your options are limited and I would not run to pay someone so quickly. I continue to be disappointed by FTers who refuse to give any advice for free.

Delta
The only Skyteam carriers that currently fly to DBV or TIV are Aeroflot from Moscow and Tarom from Bucharest. If you could find inventory from Canada to London or Paris, then London/Paris to Moscow/Bucharest to DBV or TIV; then back from DBV/TIV to Moscow/Bucharest to Canada, that should work with Delta miles. You wouldn't be able to fly into London and out of Paris or vice versa, so would have to train or take a revenue flight back from wherever you get off the plane, and you can't do stopovers both ways. You would have to book this as a roundtrip for 50,000 if you find low availability or fly partners.

BA
Oneworld does not offer a lot of flights to DBV or TIV either. Your options are S7 (Moscow-DME) or Air Berlin (Munich) to TIV, or BA from Gatwick, Iberia from Madrid, Finnair from Helsinki, or S7 from DME to Dubrovnik. You can also use BA miles from Dublin.
You can do any routing you want, but you pay based on distance of your flights. Flying from Canada into London will generate a lot of taxes and fees, as well. This would probably be the most expensive option. I looked at a few possible routings, and they'd all be about 90,000 miles plus high fees.

United
This is probably your best option.
There are lots of flights into Dubrovnik on Star Alliance carriers, as Dubrovnik is a hub for member Croatia Airlines (which is perfectly fine to fly). In addition, there are flights on Austrian, Lufthansa, and SAS. Add in that Air Canada is a Star Alliance member and I'd imagine you will find a ton of options. There is nothing to/from Tivat, though. But thats an easy ground trip.
The routing would work similar to the Delta routing (cant fly into London out of Paris or v.v.)
YYZ-London or Paris, London or Paris to Dubrovnik (nonstop from Paris or connecting from London); Dubrovnik to Toronto (likely via Munich/Frankfurt or Vienna).
I just looked on United.com, and there are plenty of dates with wide availability going from YYZ to DBV and vice versa, as well as YYZ to Paris and London. The trip would be 60,000 roundtrip.

Note many of the flights to the Adriatic are seasonal and may not be loaded into the system yet or available exactly when you want them.

Good luck.

I agree, I went JFK-FRA-ZAG (spent 3 nighst) then to DBV-(Destination) -FRA-LHR-JFK (the LHR-JFK was on VS when it was a partner with CO/UA)

The only problem with Crotian air is they have but a handful of A-319s = my friends who went FRA-DBV had an 8 hr wait till a plane arrived. Crotian is mainly puddle jumpers, and they can sub them with no probs unlike the 319s. So a way around that is to stick with LH where if theres a problem they can simply roll out another plane , or make sure you arent far from DBV so that you know it will be a puddle jumper

I would look at YYZ-LHR then train it to Paris and Paris-FRA-DBV, just keep in mind OP every airport you hit in Europe will charge you for Departure taxes so you want to keep it to a bare min

We used United miles to go ORD-DBV via DUS (flying LH) with DUS-DBV on Croatia Air. It all went smoothly even though we had a very tight connection in DUS. Kudos to LH for our bags making it on a 30min connection there. The Croatian Air check-in desk was staffed by LH personnel by their uniforms.
My experience was that going to DBV was an excellent value for United miles, since the ORD-DBV fares I always saw were around $1800, so my 60000 miles (x4) were put to good use. There was good award availability. I think I finally ticketed in Nov for the following August for 4 tix.

We couldn't avoid it, but I'd recommend not going during August. DBV was really hot this month.

Montenegro is an easy day trip from DBV via rental car ($80) or tour bus ($80/pp).

As noted above, this would not be a valid routing. For it to be a stopover, you have to land in London and leave from London, or land in Paris and leave from Paris. You cannot open jaw a stopover.

We just took a very similar trip last month, although we flew round trip from Newark, NJ. We used 60,000 United miles per ticket for 4 of us (240,000 miles total) and were able to fly the following journey:

FLIGHT INFORMATION

Wed, xxJUL13 UA8 XN NEWARK, NJ
(EWR - LIBERTY) 9:00 PM LONDON, ENGLAND
(LHR - HEATHROW) 9:25 AM (04JUL) 757-200 Dinner

Sun, xxJUL13 OS452 X LONDON, ENGLAND
(LHR - HEATHROW) 9:15 AM VIENNA, AUSTRIA
(VIE) 12:40 PM A-320 Snack
Flight operated by TYROLEAN AIRLINES FOR LUFTHANSA.

Mon, xxJUL13 OS731 X VIENNA, AUSTRIA
(VIE) 12:50 PM DUBROVNIK HR
(DBV) 2:10 PM A-321 Snack
Flight operated by TYROLEAN AIRLINES FOR LUFTHANSA.

Sat, xxJUL13 OU492 X SPLIT HR
(SPU) 2:10 PM LONDON, ENGLAND
(LHR - HEATHROW) 3:50 PM A-320
Flight operated by CROATIA AIRLINES.

Sat, xxJUL13 UA115 XN LONDON, ENGLAND
(LHR - HEATHROW) 6:00 PM NEWARK, NJ
(EWR - LIBERTY) 9:20 PM 757-200 Dinner

We actually considered staying in London longer and taking a train to Paris for a few days, but opted not to do so. We had one stopover (London) and one open jaw (into Dubrovnik and out of Split, Croatia). We also stopped in Vienna for 24 hours (intentionally) since there was only one flight a day from Vienna to DBV and it left at about the same time as the London flight arrived, so there was no way to make the connection same day. this allowed us to tour Vienna for a day (and the airport is only 15 minutes from downtown Vienna).

Lastly, I would HIGHLY recommend the Radisson Blu Hotel Dubrovnik Sun Gardens. It is a truly stunning resort, only a few years old, and can be entirely free on points. We signed up for the Club Carlson credit card, which with the spend was enough for 3 free nights. Additionally, for 70 euros per night, they upgraded us to a 2BR condo with full kitchen, and it included breakfast for the 4 of us. We checked out a bunch of the higher end places in DBV, and this was the best by a long shot.

Hope this helps.