I was recently at Playa Varesse Inn. It was $90. The place is very friendly, located one and a half block of Playa Varese, walking distance to the streets in fashion, guemes and alem. There is a terrific bakery one block from the hotel with sea views, called " Boston", I strongly recommend you the croissant "medialunas" from there. From there you can take the bus or walk to the centro (casino, walking street san martin). You will take a bus towards the puerto, to the south of the city. They have a restaurant department, try to avoid Chichilo. And for good paella with plenty of seafood, try La Paella, on Entre Rios street crossing Moreno if I remember well.
Going back to the hotel, the staff is very friendly, they welcomed me the argentinian way, with a kiss and hug, and also were happy to help with tips or calling a taxi. The place is pets friendly, as they have few rooms with a little backyard.
If you want to stay in the centro of the city, I recommend Hotel Guerrero, with views of the sea and two blocks of the walking street, called san martin. It is more expensive, like $190 per night. Also very nice.
There is an office of tourism. I think they will give you lots of information on what to do in the city.
Id been in mar del plata for many years and about the beach, the point is the wind. They best is to go to 'bay areas' beaches, like bristol or varese. I like the beaches of the south, after the puerto, because you get a wonderful view of the ciity, but I dont like those beaches in other way.
To take a bus you need to buy a card, and each trip costs ARS 2. If you dont have the card, try getting into the bus and ask someone to lend you the card and you pay the ARS 2 to the person.
Enjoy your trip,