If you book normal revenue tickets most flight search engines do the heavy lifting and show you a sensible route and pricing for most destinations.
Now for award tickets few booking engines show you connecting options (united.com and the ANA search engine are probably best).
Step 1 – Find flights for award tickets using ITA Matrix
ITA Matrix lets you do a lot of nifty things. However the most basic functionality is the search for 30 days for a route. You can specific stop over options.
The lowest prices is most often the flights you want.
If you already know your airline you can also specify the IATA code and a plus under special routing codes. i.e. UA+ will only return United flights
While ITA Matrix usually has all the fares that are filed in reservation system it is optimized for the shortest route. Often these flights won't have award availability though.
Step 2 Use Openflights.org
Openflights.org is exactly what you expect a wiki appraoch to flights. It gets data from OAG but also has a number of additional flights. It has a good interface to see where airlines fly from one airport. Results are often surprising (at least for me). The data is good but can be a bit old and incomplete.
Step 3 – Wikipedia search for destinations
Step 4 Find Low Cost airlines with kayak.com and wegolo.com
Often an award ticket will get you far but you don't have enough miles to get into the next 'zone'. A good example is American Airlines award chart that will get you to Southern India but NOT to the Maldives. Often discount airlines serve nearby airports and get you where you want for small amounts of money. wegolo.com has a lot of data but also is not easy to use. Often kayak.com nearby airports function is better and includes all data from wegolo.com.
Step 5 Try whichairline.com
whichairline.com combines 'legacy' airlines and low-cost airlines in one interface. It includes nearby airports as well. I ran teh example for Moscow which is always tricky since it is served by 3 airports and many alliances serve a mix of them.