This is a vast topic, but much depends on your interests. The Imperial War Museum covers 1914+. The National Army Museum (also in London) covers everything prior to 1914. Chelsea Hospital,
next door, is also well worth a visit.
If you want a regimental museum, go to Winchester. The R. Hampshires, the Gurkhas, the King's R. Hussars, and, above all,
the R. Green Jackets are all there. If God made military museums,
the R. Green Jackets museum is exactly what he would have created.