Best solution

My daughter has a game system that outputs analog only (audio left and right plus video). Her new TV (holiday gift) accepts HDMI in only. We can't replace the gaming system (long story).

Adding or finding a replacement TV with analog inputs possible might not be possible due to return logistics (and a second set seems like overkill here), so a few question follow:

Do AVRs typically allow HDMI out from an analog input signal?
Is there a reliable conversion component to insert between the game console and tv to get HDMI from the game system?
Is there another approach to consider?

I think receivers can make this conversion, but the results may vary. You can purchase converters as well, at least I think you can. Maybe something from monoprice or RadioShack. Is the goal a hifi system or the most cost efficient connection? You may end up with a 4:3 signal with the analog video. I think the audio will be much easier than the video side of this connection.
Most used or classic game stores will sell adapters to connect these older systems.
Thank you all. Just want to make the connection, so the converter box from Amazon may be the best call.
Older AVRs most definitely would allow connection of analog video and audio inputs and then 'upconvert' for HDMI output.

My Yamaha RX-V1800 has inputs for S-VHS and composite video along w/ L/R audio inputs which can then be upconverted and outputted to HDMI.

It looks like @ss, depending on resolution of source device, but it can be done.

Newer AVRs seem to be ditching pure analog video (and audio) input from 'legacy' devices such as gaming systems, CD players, some dropping phono inputs, etc - so maybe you could find a killer deal on an older AVR that sits between eras.