Microtel Hotel, it's near the Bay and Mall of Asia (MOA), so loads of food choices. Not in Malate area, though. Don't know if rooms have balconies, but it has a pool. I think it's 3-4k pesos per night (60-80 USD). Haven't stayed there but have seen pics.
Another one I'd recommend is Hop Inn Hotel, also near the Bay, MOA and airport. Around 2k a night (40 USD, 1 USD ~ 50 pesos). Have stayed there - it's new & adequate. Owned by a Thai consortium, I believe. Lots of branches in TH.
Heritage Hotel - also near the Bay. A bit higher end but older hotel, near EDSA highway. Been there for a work function.
BTW, lots of Airbnb flats in MOA area - lots of new Condo buildings there and some units have balconies.
I think most Manila hotels don't have balconies, esp in busy areas, due to air pollution. Near MOA, the air is OK bcos of the sea breeze.
Near Malate, I don't know many hotels. I think there's a Hop Inn there too. There's H2O hotel, which is higher end. That has a pool but I don't know if with balconies. I don't go to Malate often - found it too busy, noisy, with hookers and lots of dodgy looking sexpats/ tourists (no offense, switch).
Especially near Robinson's place Manila (a mall near the Phil. General Hospital).
Check Agoda or Booking for more info.
Edit: had a look around Agoda. Couldn't find hotels with balconies in the 40-60$ Mark. I did see Shell Residences near MOA - Condo type units that they let out. Units have balconies, around 40 USD per night. The Condo complex has a pool. It's along EDSA highway and near Mall of Asia. I've seen it/passed by it along the way to MOA.
SM Sea Residences - Condo units with balcony, near Bay & MOA, 30-40$.
There's a Hop Inn near Ermita which is near Malate, the Bay and US Embassy, ~30 USD per night, but no balcony.
New World Hotel Manila Bay, Diamond Hotel, Palm Grove Hotel, Pan Pacific Hotel, Birch Tower Condos - all in that area, near Ermita/ Malate and the Bay but I don't know if rooms have balconies.
Pearl Manila Hotel - not too near the bay, 1.1 km from Bay, but near Malate, around 40 USD, some rooms have balcony, has pool. Located at corner of Taft & UN Avenues - very busy & trafficky place.