The good news is that there are lots and lots of opentype font families that provide a full Cyrillic alphabet and are easy to use with XeLaTeX (and LuaLaTeX). The bad news is that you may have to spend some time choosing which font family best suits your needs. MacOS X provides quite a few such font families; it's also fairly easy to download and activate additional fonts -- high-quality and free of charge -- that may suit your needs better than the ones that come pre-installed with MacOS X.
The main font-related package you should become familiar is called fontspec
. It provides the command \setmainfont
, and many more.
MacOSX provides an application called FontBook
. FontBook
provides a convenient (though slow) method for inspecting all installed fonts for various features, including whether cyrillic characters are included in a given font.
Here's an entirely non-representative sample of font families that feature cyrillic characters. Some fonts should already be installed on your system, while others (e.g., EB Garamond and XITS) may need to be downloaded and activated first.

%% !TEX TS-program = xelatex
\documentclass[a4paper,12pt]{report}
\usepackage{fontspec}
\setmainfont{lmroman10-regular.otf}
\usepackage{polyglossia}
\setdefaultlanguage{russian}
\newcommand\hi{Hi! Привет!\newline}
\begin{document}\pagestyle{empty}
\noindent Some serif fonts\newline
\noindent%
\setmainfont{Garamond Premier Pro}\hi
\setmainfont{EB Garamond} \hi
\setmainfont{Arno Pro} \hi
\setmainfont{XITS} \hi
\setmainfont{Cambria} \hi
\setmainfont{Minion Pro} \hi
\bigskip\noindent%
\setmainfont{lmroman10-regular.otf}%
Some sans-serif fonts\newline
\setmainfont{Calibri} \hi
\setmainfont{Arial}\hi
\setmainfont{Myriad Pro} \hi
\end{document}
.otf
, whereas many OpenType fonts are distributed in files with extension.ttf
. The answers to the second posting provide information on finding type-1 T2A-encoded font files with cyrillic characters, but nothing at all about files with extensionsttf
andotf
; the latter clearly are the main focus of the users of XeLaTeX and LuaLaTeX.