I've used this HDMI to VGA adapter with good results. VGA to RGBHV cables are pretty common and not expensive unless you need insane lengths. ...

Ballpark figure for a HDMI to VGA decoder is around 200 mA at 5 volts. That's a watt. For such a small device, you're going to expect that to make it fairly warm.

For example, your TV likely has HDMI 1.4 connections, which max out at 3,820x2,160-pixel resolution at 30 frames per second. If you've gotten a new 4K monitor, you're limited to 30fps.

HDMI is really best for connecting a PC to an HDTV. Consequently, I’d go with a DVI cable. That’ll give you a pure digital signal (VGA is analog) and a much sharper picture at higher resolutions.