yeah, parking behind the museum should be ok tomorrow. Not sure if the Kashmir will be open daytime though.
Can’t really recommend anywhere to eat in town during daytime, unless you can find a decent pub – The Noble Comb in Shipley, about 4 miles north on the way to Otley/Ilkley/airport is ok for food & is a 2-for-1 pub so should be family friendly & reasonably cheap.
Can’t recommend anything closer to the NMM, unfortunately, as I no longer live that close to the city centre. Of course there are all the usual chains, plus the usual other stuff (chinese, italian/american, etc) at the cinema complex behind the bus/railway station