Most large US banks or banks with a US presence will allow opening a US bank account reasonably easy. Call around. It is generally easier to open one in person (but if you make a trip, make sure you know what identification they require first as it varies wildly), but at least the larger banks tends to have no problems handling foreign account holders with the caveat that the paperwork can be a bit annoying.
I once opened a Chase account from Norway, and had to go to the US Consulate in Oslo to get an apostille on the application form (basically the consulate had to attach a document by seal that confirmed they had seen my id and matched the details to what I claimed on the application, and watched me sign the form - apostilles are expensive, I had to pay about $100 that time, and it's unusual to require it to be done at a consulate or embassy rather than "just" a recognised notary public).
TD Bank is another alternative I have more recent experience with - it's a Canadian bank group with branches in lots of US states, including Delaware, and a company I'm involved with had them open US accounts for a US company we set up, though we also had an account with them in Canada opened from Canada by a Canadian citizen, so I don't know how easy or hard it'd be to get an account set up by them from elsewhere - they did fedex me documents to the UK to sign, though. And didn't require any apostilles or other expensive verification.
Depending on your location, you may also find it possible to open a US held bank account from your home country by looking at which (if any) of your local banks have branches in the US (this applies in general for many country pairs, but especially if you want to open accounts in major financial centres - my old Norwegian bank has a branch in London, for example). Note that in many cases they will have "branches" that are not generally open to consumers and may not be advertised, so you'll want to check online and call their business banking people. Major international banks like Barclays or HSBC for example may often be an alternative.
It is also easier if you "only" need a dollar account as opposed to a US held account - many banks offer accounts in the major currencies without offer a general banking service in the relevant countries -, though I'm assuming you actually need a US account.
At least judging by the UK account fees SVB are horrifically expensive and seem to charge through the nose for everything. I'm not sure whether this is the case for a US-domiciled bank account though.
HSBC have a decent international banking department and can open accounts in different countries last time I checked.
