If you have to ask, the answer is you don't have enough! :)

Seriously though, just wander into any big ass bank(Chase, BOA, etc) and ask them. They have multiple tiers of private banking, depending on your wealth level. Generally the bottom tiers start around $100k and go from there. To get into the fancy tiers you generally need $1M or more of bank assets. To get into family offices, you generally need $100M or so. Though shared family offices are sometimes available at the low 30-50M range.

Just be very careful of fees. Generally the larger the private client services, the higher the fees.