One building with countless HKD200+ to 400/night "hotels" is the Chungking Mansion in Tsim Sha Tsui district of Kowloon in HK. This is a busy district where the world famous Peninsula Hotel & other 5-star international hotels are located, just a 6-minute walk away. Be warned that this Chungking building is not considered "safe" by locals.
Inexpensive hotels in HK are based on travel "peak" & "off peak" seasons or periods. A good way to check & book is via www.agoda.com I have seen clean, very conveniently located but very small room hotel at HKD400 to 500/night in off seasons. I have booked many & different hotel stays through this site with a US issued credit card and never had any problems. (i.e., The Mini Hotel in Central which is 1-year old but very very small rooms, can be HKD 500 to 1,500+/night, the YWCA near Mongkok, out of date but clean, can be HKD400 to 800/night, rooms with shared baths are cheaper).
As an American, each HK entry is no visa with a 90-day stay. As a first time visitor to HK, I'd suggest once you are in HK, buy a copy of the English language newspaper "South China Morning Post" and look for the classified section for visa services (number & types of classified ads vary from day to day) mostly through travel agencies. They will do all the paperwork on your behalf. a valid passport (I believe a passport with at least 6 more months before expiration is a major requirement for all visas for all nationalities and for all countries). The visa service from China Travel Service is most expensive. Visa for Americans, regardless how or where you get it, is also the most expensive compared with other nationalities. You can also go to the Chinese government Office in HK (sorry, I don't know the official name or address) and do the application yourself and save some money (sorry again I do not know the process or cost). I believe if the application is submitted before noon on day 1, the visa is ready in the afternoon of day 2, regardless if it's via a travel agent or at the Chinese gov. office. If submitted after 12 noon, the visa is delayed til the afternoon of day 3. I get my 2-year multi-entry visitor visa in New York city through a travel agent in Chinatown for USD190 (a DIY application is USD40 less and is not worth it since I'd need to make 2 trips to the Chinese Consulate and wait on line for hours each time). In HK, I believe the max. is a 6-month multi-entry visa for US citizens.
Another good thing to have is an "Octopus Card" for taking public transportation such as the MTR (subway), buses, mini buses, ferry and even as a debit card at some merchants. You can buy it at any customer service booth at any MTR station and I believe also available at the HK train station after the Shenzhen crossing to HK at "Lo Wu, aka Louhu port" or even the airport machines. Remember the card requires a HKD50 deposit and you can add on as many dollars as you want for rides. If you return the card (must be at any customer service booth at any MTR station) before leaving HK in less than 3 months from date of purchase, there is service charge deducted form the HKD50 deposit (no service charge deducted for cards older than 3 months). I'd suggest that you keep the card for future trips to HK as a convenience.
An inexpensive telephone card can be purchased from any 7-11 store or other "convenient stores (there's one almost on every block or 2 in HK). HKD60 or 68 will buy you a SIM card with a HK telephone number with hundreds of talk minutes. Be careful when selecting the provider (tel. co.) because not all will supply the micro SIM needed for iPhones, while some will supply a normal SIM card that can also be snapped again into a micro (PCCW is one provider that comes to mind). Such SIM cards usually allow you to make local calls at twenty cents/minute and to the USA, China and a number of other countries at the same HKD.25/minute (read the package carefully).
I have read in GoK Forum that one can extend an about to expire visa in Kunming for a just few RMB. You may want to look up that info (via GoK search in the upper left corner of the home page) and buy enough of time to search for a decent priced air ticket & hotel in HK. The Chinese "C-trip" site is a good site to search for inexpensive tickets. They have English speaking customer service that actually speaks decent English. They even accept foreign credit cards at a 3% sur-charge. I have gotten R/T tickets bet. KM & HK for as 1,409RMB, or bet. KM & Shenzhen for as low as 860RMB.