i stayed at asia a couple of times when i was in bkk. didnt notice any street dedicated to dessert. but at night, there are street food along phayathai and petchaburi roads. from the hotel front, along phayathai rd towards huachang bridge are mostly street tze char (pretty flavourful stuff); towards petchaburi rd will be a mixture of other food like wanton mee, thai salad, mango sticky rice, crepes with pork, etc. recently durian season, so there are some fruit stalls as well. soi phaya nak at the side of the hotel also has street food.
basically, asia hotel is convenient for its direct link to bts rachathewi. walking distance to pratunam and siam. canal boat stop is also near, at hua chang bridge. can use motorbike taxi or tuk tuk to tesco lotus and other places. only down side is that phayathai road is jammed most of the time. so, use the BTS, canal boat or motorbike, or walk.