Whereabouts in Brighton?
I don't think I would go as far as Eastbourne if he will be getting the train as not direct.
Chichester is nice ( although not coastal per se) - and the train can be a bit of a drag ( I commuted to Chichester from Brighton / Hove for over a decade).
If you want coastal and for that budget I would actually look at Shoreham-by-Sea ( I am biased but I live there).
For your budget you could get a really lovely house on the area called Shoreham beach. It's a shingle spit of land connected to the town by a road bridge and a glass footbridge across the river Adur.
The houses are all post-war ( due to an interesting history) - a lot of really innovative new builds and made over bungalows as well as 70s style chalets. What is lovely is direct access to the beach which is a nature reserve and a lovely bathing beach / popular with windsurfers and SUPers.
The town itself is lovely too - but it's charm is not immediately obvious. There's a lovely town centre with a flint church and a pedestrianised center with restaurants / bars and a farmers market.
The coast road through the town let's it down on first appearances - and the outskirts from Brighton are industrial before yoh get to the town proper.
There's an Art Deco airport, the river Adur and an amazing houseboat community. Lots of pubs and cafes, good schools, ok high street ( slightly too many charity shops and estate agents). But the basics like a boots and a wh smith, pharmacies and some nice chi chi shops too