Try a program called "Modeller" from Sali's lab, which lets you model missing parts of the system. The program is free to academics and has a tutorial but it's mostly driven by running python scripts through the command line. If you're looking for more graphic-friendly approach look into Prime by Schrodinger. This program is not free, but i'm sure you can get an evaluation copy to try it out.
If you just want to rebuild part of a protein, say, side chains, have a look at the WHATIF servers. If you want to model part of a protein, indeed use Phyre, Swiss-Model, or MODELLER. MODELLER might seem hard in the beginning but you will learn a lot from using it and it is in fact pretty straightforward for simple cases, they have pretty much "pre-built" scripts ready for you to download and use, you just need an alignment.