I know it gets mixed reviews but I have had a positive experience with the Blackmagic Intensity Shuttle. Pretty compact, bus powered, has a range of analog connections plus HDMI. Tops out at 1080p30, I believe though. I personally don’t have any sources I’m recording that are 1080p60, so it works for me.
They can be found use for a lot less than new. I got really lucky but I got one for $35 on craigslist last year.