Looking for a short term flat for this trip and just going on my passport right now. But will (hopefully) be going to school there next fall (2014), so will be applying for the Tier4 Student Visa (as well as the family Visa for my daughter) next year.
Sounds like fun

. Have you decided what you're going to study there?
If you will be getting a Tier 4 visa, for your daughter (assuming she's under 18), you'll need to apply for a Tier 4 Dependent visa for her, and have the required extra amount in living costs on top of your required living costs for the first year (£7,200) and international tuition fees

. However, you can only bring your daughter with you if you are studying for a masters level degree or higher (and for 12 months or more) - if it's a bachelors degree or lower, you won't be allowed to get a dependent visa for her and she will have to stay in the US.
One thing to consider for your trip here in October: will you have plenty of evidence that you are a genuine visitor, that you have a job and a home in the US to return to at the end of the trip (i.e. a letter from your employer in the US and evidence of homeownership/valid rental agreement in the US), and that you have enough money in your bank account to support yourself for those 5-6 months without working?
While visitors from the US are technically allowed to come to the UK to visit for 6 months in 12 months, whether you are actually let into the country or not depends on the immigration officer at the airport when you arrive - you need to be able to show that you are a genuine visitor and have no intention of trying to live, work or study in the UK without a visa.
As most visitors to the UK only come here for a couple of weeks on vacation, the longer you want to stay, the more evidence you'll need to show that you have ties to the US and that you are not planning to overstay or work illegally here.
If you want to be sure of being approved to enter the UK, you can always apply for a visitor visa (£80) before you fly, providing the evidence with the application.
Alternatively, have you looked into the Prospective Student Visa? It's a visitor visa that allows you to come to the UK for up to 6 months in order to visit universities in person and make a decision about which school you wish to attend.. you can then apply for the Tier 4 visa once in the UK and switch directly to it without leaving.
However, in order to qualify for it, your course must start within 6 months of entering the UK, so if your course won't start until September 2014, you cannot come to the UK on a prospective student visa until March 2014 and you need to already have been in contact with the UK universities you may wish to attend.
See:
http://www.ukba.homeoffice.gov.uk/visas-immigration/visiting/prospective-student/