I suppose your perception will depend on your frame of reference when it comes to what you consider dodgy.
I wouldn't consider Nazaré dodgy or dubious in a million years. It's a fairly ordinary middle class neighbourhood, with decent amenity. Tourists always seem to get het up about Salvador and personally I think it's the down to the demographics. They won;t admit it but many of them seem uncomfortable around such a large and predominantly black population.
That said, if walking up to the Pelourinho you may wish to exercise a degree of caution and keep to the main streets of an evening. Don't try walking up the ladeiras behind the convento or along Baixa dos Sapateiros at night.
If you want some of the signature dishes of the region try the Senac restaurant in the Pelourinho as an introduction. It's a cookery school and there's a buffet upstairs that will allow you to try a variety of foods. Good if you aren't familiar with local cuisine. O Coliseo in R. Cruzeiro São Francisco is another buffet, reasonably priced and the food is decent quality. You can see half of the local police hierarchy in their at lunchtime.
Best places for lambreta, the real signature dish of the city, are actually in Nazaré, behind the forum. Koissa Nossa on Trav.Engenheiro Allioni is my fave but it's neighbour, Lambreta.com has the same owner. There's a strip of bars along that street and a few more individual further along. It's quite safe, you are behind the Army's regional command headquarters. Great vibe in the evening and quite my favourite place for a beer. You won't find any other gringo tourists though, it's not that sort of place.
It's suffered a little from it's rise to fame but one of the best moquecas and certainly one of the best value for money meals in town is at Boca de Galinha over in Plataforma. You can either take a boat over from Ribeira or take the train there from Calçada. Just get off at Almeida Brandão station and walk up the hill. Great view across the bay into the bargain.
If you are cashed up then Sorriso da Dadá is worth the visit. Dadá is a living legend. IMO not as fun as the old Varal de Dadá in Alto das Pombas. In similar vein Yemenja in Armação is very good but pricey and longish cab ride.
Acarajé sellers all have their fan base, Some like Tania's near the farol, others favour Cira or Dinha in Rio Vermelho.
Personally I favour Dinha in Largo de Santana but largely for nostalgic reasons, it's where my wife and I went on our first date. A trip to Rio Vermelho is always worthwhile but if I'm honest and I've eaten a lot of acarajé through the years, you'll find it just as well cooked and cheaper in Centro and other parts of town. If you wander along Av Sete, you'll find a stall at Praça Barão do Rio Branco that sells great acarajé for a fraction of the price at the more famous outlets.
If you want churrasco then there's a Fogo De Chão outlet in Rio Vermelho but the best meat and value for money is at Rincão Grill in Armação. Go for lunch. h and if you want somewhere romantic, my tip is the restaurant at Solar de União . You can sit on the jetty outside and enjoy being on the bay. For something still fairly local you can always grab a bite at O Cravinho in the Pelourinho. The tourists nervously stand around the front and edge into the bar but most don't seem to realise there's a cheap restaurant in the rear. The food in the warmers at the bar has yet to kill me and you get treats like rabada regularly.
Enjoy, the food in town is excellent.