Nobody is going to be offering testing bookings for June/July in January. You are looking way too early. By then the regulations can and probably will change several times. No good booking and paying for a PCR when you only need a LFT or maybe - who knows - nothing.
Start looking around maybe a month out, if that.
I get settling in and not uprooting every couple of days, and you can as you say get to Kenilworth, Warwick, Stratford-upon-Avon (less easily), and Leicester (also not trivial) from Coventry. Even places which are not great like Coventry have some good spots. There is the old and new Cathedral of St Michael. I've never gone into the new one because the architecture doesn't appeal to me but I do love the bells in the old bell tower. When the physical cathedral was destroyed in the bombing of the night (my father's family saw the colour in the sky all the way off in Cheltenham) of the 14th November 1940, the spirit of the bombed city lived on and the bell tower and the bells survived. These bells are still rung in changes and have a lovely tone. The ruins are well worth some devotional and contemplative time. Two of the fire charred beams fell in the form of a cross during the fire and is now on the ad-hoc altar. A very moving place.
The approach to the station has changed since I managed the traincrew there but will still include crossing the ring road on the way from the city to the station. You can either go over the ring road on a bridge or under in a subway (tunnel under the road). My wife used to walk through the subway as she walked to work (and home) but was only happy doing that when enough people were around - in fact she took later trains on holidays and weekends. I'm sure it is fine but more pleasant with others. There used to be rough sleepers under the cover (harmless) but years on I don't know now.
Also Scarborough isn't a total loss either. There are two (!!) funicular cliff lifts to get down to the sand. And there is actual sand, unlike many English beaches. You can have an ice cream and walk along the front and enjoy the seaside atmosphere. Just protect your chips or cone from the seagulls! Down the coast at Whitby you can search the shore for Jet, especially after a storm... that's where the term, jet black, comes from...
I think I mentioned in your previous post about the Lord Leycester Hospital in Warwick - fits into the period you study with parts of the building going back 700 years and then the Elizabethan improvements, and up through the centuries. Unfortunately the Hospital closed to the pubic at Christmas just past for major restoration and won't reopen until summer 2023. https://www.lordleycester.com/