I went travelling last sunmer and did similar to you- hostels and then posh hotel for a week.
I took a hand luggage size suitcase for 3 months. I took:
Clothing
4 tops- 2 sleeveless, 2 short sleeved and one i travelled in
4 dresses- 2x casual skater dress, strapless dress that also doubled as a swim cover up and a maxi dress.
Two pairs of shorts- one denim, one chino.
Jeans (travelled in these)
Hoodie.
Bikini
Waterproof coat (one of those that packs really small).
Bra (plus one i travelled in)
2x knickers (plus ones I wore when travelling)
Microfibre towel (quicker drying than normal towels- just dont expect cashmere quality)
Plastic hangable washing line.
Clutch bag
2x necklaces- a cheap statement piece and everyday necklace.
Just wore the same studs for earrings
Pair of wedges and pair of fit flops. Travelled in Converse.
If necessary I would of put clothes into my rucksack when travelling to make room for a coat and winter shoes if it had been necessary. Would of managed it just fine.
Key to packing is rolling not folding your clothes. Get a suitcase with a inside zip top so you have an extra compartment.
Other:
Phone
Kindle
Camera (which i then regretted)
Charger for phone, kindle and charger (get a mutli plug)
Minimal makeup- i took a mascara, foundation and blush. Remember if your taking it on the plane with you it has to be a certain size- i did buy minatures before leaving and topped up when required.
Toiletries, first aid kit Ibrought along the way. And liquid washing soap. First stop I made was at a supermarket to buy s few bits. Instead of taking massive amounts of clothes I just washed 2x times a week at most and hung things up overnight to dry. Eventually you wont give a shit. Your away to have fun.
During our 3 months travelling we dressed up once when we went to Vegas. Rest of the time we were eating in burger joints etc and it wasnt necessary.
Check baggage allowance before you go- ie if you arent checking in bags are you allowed to take a small suitcase and rucksack on board with you?
Personally- if your planning on doing it, dont lug a massive camera around with you. I did and then found I managed just fine with my iPhone. Dont think youll need to take iPads/laptops with you- you wont have time to use them. Use your phone to send the odd email, facebook update etc. Kindle is a life saver if your going to have long trips between places.
Invest in a decent rucksack for when your walking about- not to mention youll be amazed how much you can fit in it! Go to a store and try some out- fill it up and walk around with it on for a bit and see how it feels.
For when we arrived in NY, i got my Mum to fed ex me some nicer clothes to wear in the hotel, for theatre etc. It cost me about £50 but it was stuff I wasnt lugging around for months before I was going to use it. I then brought a bigger suitcase from TJ Maxx very reasonably (would of been necessary anyway after hitting the outlet), paid to check it on the way home and got on the flight with my little one and my rucksack like on the way out.