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ShangriLa is on Charoen Krung at the end of silom. Taxi to nana sans traffic would only cost 80B. chuck him 100 and start you evening with a good vibe.
As for the directions above, turning right at the top of Silom is Rama 4 and it certainly doesn't turn into Sukhumvit.
Without confusing you with short cuts, from the shangriLa I'd expect to go up Sathorn rather than Silom, right at the top, down Rama 4, keft at Southern Ratchadapisek past the Queen sirikit Convention Centre and then you are at Asoke for cowboy, or left at the junction to roll into Nana.
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