Hot springs

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We want to experience going to Hot springs in Japan. We were thinking of staying overnight in Hakone at a hotel with hot springs but the prices are too expensive, Instead we will go for a day trip to Hakone, but dont know if we will have time to go to a hot spring there for a short time. Would we have enough time?. Or should we just do it somewhere else like Tokyo, Nikko, Kyoto, etc?. Is it the same?any recommendation for a nice place for a good experience?. Thank you.