Gangtok or to be more specific, the whole of sikkim is an exotic place for every traveller with any type of budget. my only advice is to avoid the tourist season that is the summer and durga puja holidays. if you have no problem in cold, best is to go there in december. you may actually experience a snowfall and that also for a highly discounted price at even the best of the hotels. if you are going that time then definitely avoid any type of travelling agency.
i’d gone there in dec 99. a bombay travelling agency gave me a budget for a couple for 5 days at around rs.10000/- from shiliguri (nearest rail head) to shiliguri. i’d completed that part in around rs.5000/- staying in a very good hotel and travelled all along in car without sharing.
if you want to see snow go to gangtok and changu lake (not sure about spelling)in dec. if you want a calm and quiet honeymoon go to pelling/rabangla. if you want adventure go for trekking (with various options tarting from beginners to very advanced) in summer. the choice is yours. in case you need any info for free you may contact me.