I actually would recommend puNES instead of Nestopia since Nestopia has significant accuracy issues such as several APU and CPU functionalities and MMC3 mapper issues. I've found puNES to be the most accurate standalone NES emulator around. There's also multi-system emulators like BizHawk but they may be a bit confusing to newcomers.
For those who are tech-inclined; stick RetroPie on a Raspberry Pi and gift it to fellow gamers this holiday season. Much cheaper than an NES/SNES classic ;)