I would base yourself as close to St Pancras station as possible.
Cambridge can be easily accessed from Kings Cross station (which is literally next door to St Pancras). Use http://www.firstcapitalconnect.co.uk to travel to Cambridge. An anytime day return (which can be used at anytime hence the name) is £34.10 (to rip off all the tourists I presume), whilst an offpeak can be had for £23.70, but the first train it can be used on is the 09:44 departure from London.
For Brighton, take a direct train from St Pancras International (just type st pancras into the search on http://www.firstcapitalconnect.co.uk/) to Brighton. An anytime day return is £24.10, an offpeak day return (where the first train available on this ticket is the 09:40) is £16.40
Apart from the castle, there's nothing else in Dover of interest, so considering stopping off in Canterbury on the way back by. To get to Dover however, take a train (http://www.southeasternrailway.co.uk/) out of St Pancras station. A peak return is £37.40, an off peak return is £33.30 so in that case there's not a lot in it (and besides, you'll be going against the traffic flow on this route).
For the Seven Sisters Cliff, I would suggest taking a Southern train (http://www.southernrailway.com/) from Victoria to Seaford (You'll probably have to change trains in Lewes) and the total trip is between 1:27 and 1:31 in duration. If you are happy with buying an anytime day return ticket for £30.80, you can take any train you want. If you want to save money by travelling only during offpeak, the first train available is the 09:47 which will dump you in Seaford at11:14, but if you buy two offpeak singles in advance for £5 or £10, the total round trip (provided you return during offpeak hours) would be as low as £10, instead of £30.80. To access Victoria from the St Pancras area, take the Victoria tube line from St Pancras to Victoria direct.
Can't help with accom, apart from that there's a http://www.travelodge.co.uk about 300 metres down the road at London Euston.
