Price: 1500 - 3000 bath. Look for deals on Agoda, Hotels and so on. Trip Advisor is good for ratings and you can see traveler photos.
Closeness: anywhere between Soi 2 and Soi 23 is ok, but the closer to the NEP (or SC) the better. Careful not to end up too deep in a Soi. There are some ok hotels on Soi 11/13 which IMO is too deep. For first-timers, I recommend Majestic Grande. Majestic Suits I hear is good value, if you don´t need a pool.
Openness: Google the name of the hotel + Bangkok + "guest friendly" or "bar girl friendly" or something like that. If in doubt, send them an email and ask about their joiner policy. Or post a question on forum under the hotel section.
Safe: I have stayed in about 15 different hotels in Sukh and have not seen a room without a safe. I assume it´s there and don´t bother asking. Worst thing that could happen is that you will need to find an alternative storing.
Generally, consider what you need and what you are willing to pay for. There is no need to pay more for a hotel with a pool if you won´t use it. Do you enjoy staying at a fancy hotel, or are you just looking for a bed to sleep? For me, the hotel is part of the experience. I enjoy bringing a girl to a nicer hotel, and I am willing to spend a bit more (but I do regret those 9 nights in a row at Sofitel).
I also move around a bit. Changing hotels is not a big effort for me, so I don´t mind. Then you can split your time between the NEP area and the SC area. You can also book a cheaper hotel half of the stay and then live a life in luxury spending what you saved on a nicer one the second half (important that it is in that order).
Does this mean that you are about to book your trip? :)