HDMI is only important if you want video and audio with just one connection. Since nVidia cards do not have an audio processor (AMD/ATI cards do) this is a non-issue.
Also integrated monitor speakers sucks anyway, although there are some monitors with an audio output jack. Meaning you connect the HDMI cable to the monitor and then connect external speakers to the monitor.
HDMI can be used for gaming. Technically speaking the only difference between DVI and HDMI is the physical connector and the fact that audio cn be transmitted over the HDMI cable.
If you want to watch a Blu-Ray movie then all you need is a video card and monitor that are HDCP capable. All modern video cards are now are HDCP capable, most monitors are HDCP capable. All monitors with HDMI connections have this capability and either DVI or HDMI ports can be used.
Well I don't buy LCD for their gaming performance. I buy monitors for overall quality which is why I dished out $1,200 for my 26" NEC LCD2690WUXi about 14 months ago. It has an average of 32ms input lag (2fps).
If you want a good monitor that does not use a cheap TN panel, then consider the Dell 2408WFP revision A01 which uses a S-PVA panel. The original version had somewhat high input lag, the A01 revision is supposed to have lowered it, but I haven't seen any reveiws of it.
Mentioned this in another thread, but you can also consider the HP w2228h. 1680 x 1050, 3ms response, DVI/HDMI/VGA input (can switch between multiple inputs), a USB hub (I use it for mouse and keyb), and a stand that pans up and down and rotates entire display 90 degrees for portrait mode! Got it for $350 a few months back.
Unfortunately, while prices have dropped, can't seem to find a US retailer. You can start at HP's product page.
Its an ACER 24" monitor, gotta be one of the best you'll ever see for its price. At TigerDirect.com its at around $260 and thats an amazing price for its performance, 2ms response time, 1920x1200 resolution, hdmi, dvi and vga inputs, 50000:1 contrast for solid colours. and its nice and big 24"!! I highly recommend the monitor, im gonna pick it up soon for my gaming rig.. using a 26" LCD TV, 1080i.. having some connection problems with it using an HDMI cable, sometimes the signal just doesnt pickup, the resolution doesnt go past 1280x1024 without bugging out on my TV too, so I want a use a real monitor using a DVI cable for solid gaming, and I think this monitor is my ticket to epic gaming!
Playing on an AMDPhenomX4 9650QuadCore2.30GHz, two HD3870s in Crossfire,NZXT Tempest case, 4GB 800MHzRAM, 7200RPM 500GB HD, 750WPSU, Asus M3A78-T mobo.