Given that you're coming right at closing time for the season, I would go higher elevation on the second week and try Alta/Snowbird.
Thank you. Where would be the best/cheapest place to stay?
By the week of April 6 lodging at all the resorts is going to be heavily discounted, if you are going to ski Snowbird/Alta, you could stay right at Snowbird (cliff lodge,etc.) although not much at Snowbird other than the mountain, the other option is to stay put in Park City, about 45 minute drive but you got the restaurants, activities, mountain atmosphere (and indeed great rates, I for example drop rates dramatically offering 3 bedroom luxury ski in ski out accommodation with pool etc. for $995 that week, see www.sundialatcanyons.com, or non ski in ski out for $499/week, see www.vrbo.com/388097)
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