Have a Sony Android TV. I get basic cable via a really old school cable box that is plugged into HDMI input. Are there apps out there in the Google Play store that can stream/display TV that comes in via that port? Something with a better TV guide and possible DVR features?
No. When you are using an HDMI input you are bypassing the android platform and the TV is outputting video directly from whatever source you feed it. Additionally, signals sent over HDMI are commonly protected by HDCP which prohibits recording. Your best bet may be to see if your cable provider provides a streaming app for android (many do these days).