Where to buy an Oyster card and where to get the refund after a short time of use

Note that there is a specific option for a Visitor Oyster card. This is the same as a normal Oyster, but you pay a small fee (£3) to buy it instead of a deposit (£5) on a regular Oyster.

One big advantage of a visitor Oyster is that 11-15 yr olds can get the child discount without needing a Zip photocard. According to https://visitorshop.tfl.gov.uk/help/visitor-oyster-card/ :

Children aged 11 to 15 can also use a Visitor Oyster card and benefit of the Young Visitor discount – this can be added by a member of the staff at most Tube stations in London and offer children 11 to 15 years old half adult pay as you go rate for up to 14 days.

In January 2016, you could not get a refund within 48 hours.

During our visit to London on the 1st of January 2016, we found out you can not get a refund for your Oyster card through a machine at the station within 48 hours of buying it. This was confirmed by a Transport for London employee, but I could not find this requirement in writing, now or then.

On the site of the London Travel card you find the prices of the travel cards and the Oystercard caps for the same zones.

Travelcard Prices (these are subject to change and prices are controlled by TFL)

Select type Day Anytime Price Off Peak Day Price
Adult Zones 1-2 £12.00 £12.00
Adult Zones 1-4 £12.00 £12.00
Adult Zones 1-6 £17.00 £12.00

Oyster Card Capped Prices

Select type Day Anytime Price Off Peak Day Price
Adult Zones 1-2 £6.40 £6.40
Adult Zones 1-4 £9.20 £9.20
Adult Zones 1-6 £11.70 £11.70

So yes, you are right to want an Oystercard for two days use of a travel card, even if you do not get the deposit refunded.

You pay a £5 refundable deposit to get an Oyster card. You can get an Oyster card at any tube station as well as at several other locations.

This site explains the refund.

If you don't have a contactless and Oyster account, you may be able to get a refund from a Tube station ticket machine if your card has:

No more than £10 pay as you go credit
No valid season ticket

It might be worth noting that these days any contactless credit or debit card can be used in place of an Oystercard. You will be charged the same as if it were an Oystercard. However, teenagers may not yet have their own bank account and debit card, and not all cards are contactless.

If you have multiple cards make very sure that you choose one and only one card to travel with. Otherwise you may be charged two penalty fares for touching in with one card and out with a different one!

If you are eligible for any concessionary discount (child, railcard, &c.), DO NOT use contactless, since you will be charged the full fare. Instead, always obtain an Oyster card and register your entitlement to a discount at a ticket office (National Rail stations in London can usually do this).

You can get an even cheaper version of the Oyster Card if you're buying it online before arriving in London. Check this guide (to airport transport from Stansted) where there's some info about the online version of the oyster card: http://londontravelhacks.com/transport-stansted-airport-london/