unfortunately, ive never been to santiago but there is plenty of info here about places to stay and there are lots of experienced posters that will be able to point you in the right direction.
as for santo domingo...check out the following:
Coco Boutique Hotel About
Hotel Mercure Comercial Santo Domingo: book your Mercure hotel in SANTO DOMINGO
also check out...
Hotels In and Around Colonial Zone, Santo Domingo and Dominican Republic
ive had friends stay at the hotel discovery and the hotel conde de peñalba and said that they loved both. im a big fan of the coco boutique hotel because its a beautiful, new hotel, its on a quieter street than the others, the owners are awesome and its only about a 3 minute walk to calle el conde and dozens of shops, restaurants, bars etc... plus they have the most amazing roof top patio!
as for transporation...i walked everywhere because i spent most of my time in the zona colonial and gazcue but anywhere else i took taxis...especially at night and it was well worth it.
good luck and have a great trip!