To get to Stonehenge by public transportation you would take a train from London to Salisbury and a bus from there to Stonehenge. For details, see this page on the London Toolkit site.
Train fares in the UK vary widely and the price of walk-up tickets can be very high. Sometimes same-day return (roundtrip) tickets are only slightly higher than single (one-way) tickets. Sometimes you can get cheap fares by booking in advance, but those tickets are for a specific departure date and time and are non-exchangeable and non-refundable. If you want help with advance booking, just ask.
London-Salisbury: £31.30 for an anytime single ticket, but only £32.80 for an anytime, same-day return ticket. No discount for advance booking.
London-Bath: Walk-up fares are £74 each way, making a total fare of £148! However, by booking in advance you can get a fare as low as £9.50 each way.
Transportation in the cities: For London each of you should buy an Oyster card, load some pounds on it, and use it as a pay-as-you-go card. Use it for the Tube (London Underground), the bus, and the Docklands Light Railway. The bus is your only option in Dublin. For Paris buy ten-ticket carnets as needed and share the tickets. Use the tickets for the metro (subway), the RER in zone 1, and the bus. In Berlin you can buy passes that are good on the U-Bahn (subway), S-Bahn, trams, and buses. I don't know anything about public transportation in Prague.