We are 3 adults, £3,000 would last us 4 weeks no problem. We average $100/day when staying offsite. Thats for all our meals (don't eat breakfast) snacks and bits from supermarket.
Main thing to do is collect vouchers, register with restaurant wesbsites, enter your Birthdate for a day or 2 before you leave and they will send you vouchers for free meals/desserts/discounts.
Lunch in parks always cost us around $30, evening meal anything from $25 at Sweet Tomatoes upto $60-70 at Cheesecake factory.
Restaurant.com vouchers can save money, buy when on sale, I paid about $4 for a $50 voucher for House of Blues.
If you have a good credit rating I would apply for a fee free credit card, I use Post Office, you can spend abroad with no fees, if you really want to take travellers cheques and cash then take about £1500-2000, leave the rest in you bank account and use the credit card, otherwise you are paying to convert to $'s then back to £'s. Personally I only use my card, today if I were spending in Florida I would get $1.55/£1 but swapping in $'s I would only get about $1.50.
Most people I know take too much on their first trip but we all do things differently, some spend a fortune shopping, we hardly spend anything, some eat in expensive restaurants, we don't, some drink alcohol with every meal, we don't, we are all different.