You could, but it's about a 3 mile walk just to get to the market. I was living in the Residence Inn for a few months near the La Quinta, and we would often drive downtown. Street parking is free after 6pm, and if that fails, we could always find parking in the lot on North Market St. or the Visitors Center on Meeting St. Parking is also free around White Point Gardens, so you could walk from there. But if you are without a vehicle, I'd suggest taking a taxi. The views walking around "downtown" are much nicer than getting there from La Quinta.
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