Drawing cash as UK citizens while visiting US

While you can go through the hassle of opening a US bank account, is there a reason you aren't just using your credit cards and a normal GBP bank account in the US? You'll want to check with your bank on what fees they charge, but most UK ATM cards and credit cards will simply work in the US. (Avoid using credit cards for ATM withdrawls, due to the high fees and interest.)

Assuming your bank participates in the normal ATM networks, you can just use an ATM with your debit card and the currency will be converted automatically. For a Barclays account, you can use Bank of America ATMs for free, and there are ~16,000 of those around the country. There's no requirement for a dollar-denominated account.

Most hotels, restaurants, and shops will take your UK credit cards, sometimes with a bit of temporary confusion over swipe vs. chip and signature vs. pin.

I would recommend against traveling with $3,000 in cash. It's not prohibited, but it could easily be lost or stolen, which would put a damper on your vacation. It could also appear suspicious to customs or law enforcement.

To add to the answer by Zach - if you have time before going, you could consider applying for a Halifax Clarity card which has no foreign currency or atm fees. You may not want to use it to withdraw cash too much, as interest is charged from the day of withdrawal and withdrawing cash using a credit card may harm your credit rating, but even only using it for purchases could reduce the cash you need to carry and so ease your concerns.

(Apologies if this should be a comment - I don't have enough rep to make one.)

There are jurisdictions in the States which allow law enforcement to confiscate assets, including cash, if they believe they may be the proceeds of illegal activity. There is no need for law enforcement to give a reason at the time of confiscation, and the procedure for getting the assets back is long and difficult. The fact that such seized cash often goes into the police budget doesn't help. Carrying large amounts of cash has been used as justification for seizing that cash.

Such events are rare, but are just one more reason not to carry large amounts of cash.

Consider travelers checks as an alternative to using your bank card to withdraw cash, or relying on card payments everywhere. Many banks will convert travelers checks for you, with ID and a signature. Carry your $3000 in travelers checks and visit bank branches to convert $500 at a time (or however much cash you feel comfortable carrying). The process is described here. From personal experience I also know that you can deposit travelers checks directly into a bank account, if you choose to open one in the US, for no charge.

I would not advise traveling in the US with no cash at all. There are plenty of cash-only businesses in the US. For example food carts or even large cafés in cities (here's a popular New Orleans one for example). More commonly, they may have minimum amounts for card transactions. ($5 or $10). Parking meters in many places may require cash. If you go camping in certain places, the camp store may only take cash (this has happened to me once). You also don't want to be caught without cash at toll booths that don't take cards.

RE: Comments about travelers checks incurring forex and transaction fees:

1. In my experience, you can buy travelers checks denominated in USD from your home country and pay the prevailing rate of exchange. My bank in my home country (ICICI Bank) didn't charge me anything for the checks themselves (admittedly they might have made up the costs with the forex rate spread).
2. At no point did I recommend paying for stuff at businesses with travelers checks. Cash them or deposit them into a bank account that you open in the US. In my experience there was no charge for this at Wells Fargo Bank.
3. I haven't done any price comparisons between the charges on withdrawing cash with a travel card vs travelers checks. Obviously if you find that banks charge higher fees to cash travelers checks than ATMS charge on foreign debit cards, don't use travelers checks.

The USA is very credit card friendly. Cash is not required for most stores, restaurants, motels, gas, etc. Why not just pre-fund your credit card with that 3000 and use the card.

I'm a UK citizen who successfully opened a US bank account when I was there. All I needed was my passport. I use internet banking to control it.

However, there's a new online "bank" called Revolut which looks worth investigating. They claim you can spend in GBP, EUR or USD at the push of a setting in a mobile app ...

Uhm, are you sure about the not being able to get money from an ATM in the US? There are cheaper ways, such as the already mentioned travel cards, but I just tell my bank I'm going abroad and that is it. I just have a debit card with a free student account with NatWest, and I doubt there are accounts with fewer features and abilities.

Having said that, I did recently bring a large amount of cash (<10,000 USD) into the US with no problems. If you are in London check the exchange booth in Covent Garden and haggle with them for a good rate. I have extensive experience with changing GBP to USD in London I can assure you that the rates there are very good. Certainly better than the rates a bank would give.