Silicon Valley Bank is a great bank to look into. If you're planning to offer card based services (on the mobile or web), with great APIs, then CBW Bank out of Kansas is also a great option. For most cases, SVB is the best go-to bank for high-tech startups and they are based in SV and understand tech very well.
The best bank for a high tech start-up is the bank that is willing to give a start up money in the first place.
Put on your best feel-good-outfit (shower first ;-) and then with all the confidence in the word, and your plan, get off your but and go knock on doors... banker's doors. Okay... call first and make an appointment, bankers don't typically meet with walk-ins.
I have no idea how good or bad your credit history is, how much industry experience you have or how much Joint Venture Capital you already have in your pocket... so there's not much more I can say... except this... go make it happen. Bring your pitch, your vision, your plan, your numbers, your research, your data, your marketing plan, your current revenues... your guts! Be prepared for a lot of questions, and most of all, be prepared for the all inspiring word... NO.
With every NO you hear you'll learn a new lesson... and then start again.
Rumour has it that Walt Disney knocked on over 100 banker's doors before he found someone who believed in his idea... what makes you think you're not going to have to do the same ;-)
If you don't believe in you, don't expect a bank to invest in you...
Where are you located? There are a handful of banks in the LA area that are diving into the silicon beach movement. Otherwise, as others have said, Silicon Valley Bank has made its name in that industry