There is always “rain in the forecast” in the Caribbean, its what keeps it green.
You might get a midday shower - & great opportunity to duck under cover around the bar or take a lite lunch. It will also rain during the night, but you will probably not notice other than some wet grass. Its the rainy season now & you might be unlucky to have a day of rain, but I’ve been at this time & had practically no rain worth mentioning. Looking at the forecast for Castries for the next 2 weeks its a typical mix of sun, sun & showers, that means as I say above.
Most places around the tourist area’s have good restaurants, you will soon get chatting to hotel staff, other guests & locals for recommendations. Look out for the street parties called ‘jump ups’ as they are really something to see & sample the food; Rodney Bay is at the top end of the island & is nearby/attached to Gros Islet & I’m sure they have a jump up. Last time I was there I found a good one at Anse-La-Raye, it was all fish, fish, fish & would go back in a heartbeat just for that.
You will be able to get an island tour organised locally, all hotels will either book or advise you on this. Ask about hiring a taxi for an all day tour, its not that expensive. If you are adventurous rent a car, but beware, you need to be able to read maps as the local road signs are few & far between.
A main attraction on St Lucia is Soufriere & the Pitons, its the-e place for the most stunning scenery & forests. Their used to be a square rigger sail boat that did a day trip from Castries to Soufriere, Castries is a taxi or bus ride from Rodney Bay. Bus tours of the island will call at Soufriere, so you get a good look & a walk around the Pitons, the nearby botanical gardens & volcano. The town is an interesting place to wonder around, we’ve been to Soufriere to just spend the day there.
I would say enjoy yourself, but that is impossible not to do so.