Hi Flippsy
Your best bet would be to head up to Shoreham - trains/buses every 10 minutes or so and is only 6-10 minute journey. Buses straight along seafront. Trains from Worthing Central every 10-15 minutes or so.
Shoreham:
Estuary of River Adur - better for low/med tides but very accessible and is in town centre of Shoreham where you'd get off bus - plenty of places for coffee and a shop!
Shoreham Beach/Widewater Lagoon/sea watch - not too good if weather very windy - get off bus at town centre, cross river and head towards beach - keep walking West (about 15-20mins) along beach and you'll hit Widewater Lagoon - but not very much around here and you'll need a decent scope for any meaningful seawatch
I'd recommend the following for the greatest diversity of birds and not so dependent on tide/weather:
Shoreham/ River Adur - get off bus at town centre on opposite side when you cross the river by train or bus. (slightly longer walk from train station) - 2mins over the main footbridge to the houseboats on opposite side. Walk up bank as far as you like - if tide out, then plenty of gulls, waders, passerines/migrants nr. houseboats and gardens etc - keep walking towards Shoreham Airport (north) staying on river bank towpath past houseboats (you'll have to cross the main A27 before Airport but footpaths immediately continue on other side of road, just keep following footpaths along river) - Chance of Kestrel, Hobby, Buzzard, Reed Bunting, Stonechat, Reed Warbler and Sedge in reed beds, Kingfisher, Lapwing and Meadow Pipit etc - on river, possible Grebe, Cormorant, ducks, gulls, few waders - double back and return to where you started - - return journey time about half an hour leaving a good hour and half for birding and more than enough time to do this walk.
PM me if you want any further info
(Other possibililities: Arundel WWT - takes longer about 40 mins each way by train and 1 change required) Pulborough RSPB - takes the same, also change required)