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Keio Plaza hotel is more suitable for family travel. The rooms are more expensive, and the hotel more traditional compared to Shinjuku Washington - mainly a business hotel with very small rooms (compared to Keio Plaza).
As to hotsprings in Tokyo, you can try the Oedo hotsprings at Odaiba - take the JR Yamanote line to Shimbashi, then ask for directions to the Yurikamone monorail that takes you to Odaiba. The Yurikamone line is a loop train, and one of the stops is closest to the Oedo Onsen. Bear in mind this hotspring feels more like a movie-set, and doesn't feel like a traditional hotspring bc 1) you pay by a electronic card that's like an Octopus card (and you pay when you check-out), and 2) they have shops and food-courts like you'll find at an amusement park (like Ocean park). But if you want to experience a hotspring without going too far from Tokyo, this is probably the best place. You can even spend the night there (they charge extra for every add'l 2 hours after midnight).
One other thing, when you take the Yurikamone train, remember there is a walkway that cuts across the circle -- if you walk from one side to the other using the walkway (about 3-5 minutes), you pay 1/2 the train fare.